In our opinion, if Control Theorists were actually interested in implementing a Robust Control, they would embrace the work of the IEEE Reliability Society (as it has evolved since the end of WWII) by also viewing the problem at a higher level involving the same constituent components participating within the principal path of implementing the solution and also utilize:

	Reliability calculations using Mean-Time-To-Failure (MTTF) associated with each of the main components occurring/participating in postulated alternative control system architectures to achieve the same specified goal that is aspired to;
	Availability [i.e., reliability with Mean-Time-To-Repair (MTTR)] for the above including sensors and transducers and actuators;
	use of triple hardware redundancy;
	use of voting between components (for three or more identical components);
	benefits of "warm standby system" versus "cold standby system" components;
	"m-out-of-n back-up" with identical components or identical sensors and actuators, where m < n;
	"mid-point select strategy" (where warranted for three or more identical components or identical sensors);
	algorithms for "real-time detection" of component or sensor failures;
	Inclusion and evaluation of the two types of decision errors incurred: "Probability of Miss" and "Probability of False Alarms" associated with the above detection algorithms, where Probability of Miss = 1 - Probability of Correct Detection;
	Use of system reconfiguration to meet goals (and [when things go wrong] not merely resort to use of (MIT Aero. & Astro. Prof. John Deyst's) "analytic redundancy" (Deyst, J. J., A Design Approach to Highly Reliable Flight Control Systems, The Charles Stark Draper Laboratory, Inc., Cambridge, MA, 1975; Montgomery, R. C., and Price, D. B., "Management of Analytical Redundancy in Digital Flight Control Systems for Aircraft," AIAA Paper 74-887, Aug. 1974), which should only be a temporary stop-gap measure for failsafe behavior, especially since "analytic redundancy" frequently requires (i.e., resorts to) more processing (and consequential time delay) to obtain the missing sensor information fro m the equations that model and describe the situation and is therefore more fragile but still desirable to have as a back-up and internal cross-check or as a type of sanity-check on existing unfailed sensors as well). It is an excellent idea to utilize and exploit "analytic redundancy";
	Use of more realistic "3-state switches" in such reconfigurations, rather than use "ideal switches" (being idealizations that never miss and never false alarm), as should be considered in whole system or entire system Reliability calculations.
	Truthful and vigilant robustness needs to consider all the above aspects as well!

 An example on how to handle such considerations is found in: Kerr, T. H., “Failure Detection Aids for Human Operator Decisions in a Precision Inertial Navigation System Complex,” Proceedings of Symposium on Applications of Decision Theory to Problems of Diagnosis and Repair, Keith Womer (editor), Wright-Patterson AFB, OH: AFIT TR 76-15, AFIT/EN, Oct. 1976, sponsored by Dayton Chapter of the American Statistical Association, Fairborn, Ohio, June 1976. 

For failsafe or Fault-Tolerant computer capabilities, look to Stratus Computers (now Stratus Technologies with its [Virtual Operating System-VOS] and EMC https://www.delltechnologies.com/en-us/index.htm?gacd=9650523-1073-5763017-266683695-0&dgc=st&msclkid=911afd35b7811b5d0e39a256c5dc0dab&gclid=COPC7oKz8OsCFULxswodhf0OuQ&gclsrc=ds)
locally in Massachusetts and nationally to Tandem Computers and Sequoia (fault-tolerant Unix systems) in California. They possess hardened operating systems, onboard diagnostic tools, and sophisticated workload-management software that complements the hardware redundancy. Among other things, such fault-tolerant software is designed to prevent the loss of data during failures and to manage tasks such as forced switchovers from a failed system.

See IEE Proceedings A - Physical Science, Measurement and Instrumentation, Management and Education - Reviews ( Volume: 128 , Issue: 4 , pp. 257 - 272, May 1981). Abstract: The paper reviews the methods by which reliable processing and control can be achieved using fault-tolerant digital computers. The motivation for employing such systems is discussed, together with an indication of current and potential areas of application. The features of fault-tolerant computers are described in general terms, together with a system design procedure specific to the development of a reliable computer. The adherence to a well structured design methodology is particularly important in a fault-tolerant computer to ensure an initially fault-free system. In order to follow this design procedure an intimate knowledge of the following subject areas is required: fault classification, redundancy techniques and their relative merits and reliability modeling and analysis. These topics are covered in the paper, with particular emphasis being placed upon the implementation of hardware, software, data and time-redundancy techniques. Examples of fault-tolerant computers proposed and produced in the last decade are described. The availability of Large Scale Integrated circuits (LSI) and, in particular, microprocessors will have a profound effect on the development and application of fault-tolerant computers. The implications of using LSI in this area are therefore discussed including a brief description of two fundamentally different approaches to the realization of a fault tolerant microcomputer. https://ieeexplore.ieee.org/document/4644988  

Also see: Fault-Tolerant Computing 1 This chapter is based in part on portions of Chapter 8 of “Computer Hardware/Software Architecture,” by Wing N. Toy and Benjamin Zee (Prentice-Hall, 1986), and “Microprogrammed Control and Reliable Design of Small Computers,” by George D. Kraft and Wing N. Toy (Prentice-Hall, 1981) in Advances in Computers, Elsevier, 1987.

Robust Control methodology (apparently a "new toy" of control theorists in the last 30 years is evidently of limited applicability in practice since Robust Control implementations have a sluggish response that few applications can tolerate other than those in the process control industry and even then this theory is stymied by presence of nonlinearities, time-varying parameters, or noises).

This new (frequency-domain only) predominately linear Robust Control approach provides NO new solutions NOR additional applications that it can solve beyond what previous theory already adequately handled (& handled exceptionally better for nonlinear, time-varying, noisy systems, and real systems of higher dimensional state sizes). We acknowledge that there are indeed a few examples where Robust Control does, in fact, handle a "non-linearity" present in only one loop, "time-varying" present in only one loop, and "noisy systems" present in only one loop; but, apparently, can only handle one-situation at a time but only by "heroic" efforts to date! 

While I am not intimidated by measure theory, nor by Lebesgue integrals in rigorous probability theoretic considerations, nor by other stochastic integrals such as that of Ito or Stratonovich or MacShane, nor by exotic norms in a Banach Space nor exotic inner products in a Hilbert Space, I fail to see any enticing overriding lure of Hardy spaces, and especially H^∞ for control and/or estimation. I am satisfied and happy with L¹ or L² convergence or other L^p spaces, and conjugate exponents: 1/p + 1/q = 1 for related pairs of Lebesgue integrals, L^∞, and Essential Supremum. I am definitely not impressed by "Robust Control" and all its apparent pretensions. However, some useful motivation for its use is provided here: https://en.wikipedia.org/wiki/Hardy_space  and, subsequently or consequentially, here: https://en.wikipedia.org/wiki/Control_theory. Notice that the language is indeed that of "process control": slow and steady wins the race as in the story of the "Tortoise and the Hare" (so I did not exaggerate in my earlier criticism of Robust Control or H^∞ estimation as having an inherently sluggish response similar to the characteristic response of an "over damped" system rather than to the preferred  "critically damped" 2^nd order LTI system that does not exhibit ringing oscillations nor overshoot but quickly and smoothly goes to the final target state in response to the most recent set-point value submitted). While we understand that L^p spaces have pathologies when p < 1, that H^p spaces don't exhibit when p < 1 (useful for further mathematical analysis but not related to Control Theory applications [even for process control], we are less enthusiastic concerning use of H^p spaces for practical engineering applications).

For the inner and outer loops of Fighter Aircraft guidance and control, several generations of linkages have evolved since Generation 1: pneumatic linkages and mechanical levers to exercise control actuators; through Generation 2: fly-by-wire (electrical cables) to exercise control actuators; to Generation 3: fly-by-light (i.e., fiber optic links) to exercise control actuators. Fiber optic cables would previously be bleached and turn cloudy (interfering with successful communications transmission) upon exposure to a nuclear environment unless they were doped with a "Halide" such as fluorine. There are now more modern solutions to that historical problem.  

M. G. Safonov and M. K. H. Fan, eds., Special Issue on Multivariable Stability Margin. International Journal of Robust and Nonlinear Control, Vol. 7, pp. 97–103 (1997).
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.731.5673&rep=rep1&type=pdf 

Kevin A. Wise, "Bank-to-turn missile autopilot design using loop transfer recovery," AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 1, pp. 145-152, Jan-Feb. 1990.
https://arc.aiaa.org/doi/10.2514/3.20528 
Published Online:23 May 2012 https://doi.org/10.2514/3.20528  
As TeK Associates has observed or warned earlier here and elsewhere, that Loop Transfer Recovery (LTR) for LQG can only be invoked or implemented for LTI (Linear Time Invariant) systems. This is not likely the case for Bank-to-Turn missiles (except, maybe, only for one mode as a less realistic case).

Christopher I. Marrison and Robert F. Stengel, "Design of Robust Control Systems for a Hypersonic Aircraft," AIAA Journal of Guidance, Control, and Dynamics, Vol. 21, No. 1, pp. 58-63, Jan-Feb 1998.
https://arc.aiaa.org/doi/abs/10.2514/2.4197 
Published Online:23 May 2012 https://doi.org/10.2514/2.4197  

Perhaps use of "Gain Scheduling" of various PID controllers (optimized for useful control of specific regions of the linearized nonlinear system) will 
suffice for many useful practical applications. Smooth transitions in switching between different design "set points" will also need to be included in the 
implementation. Finally, the utility of the particular "Gain Scheduled" PID implementations should be demonstrated by copious simulations of the exact  
nonlinear system, as controlled by the PID Gain schedule, to verify that the resulting design is adequate for the intended nonlinear application.

For more insight into "Gain Scheduling", please click on:

https://www.mathworks.com/videos/gain-scheduling-of-pid-controllers-68883.html 

https://www.mathworks.com/help/slcontrol/ug/gain-scheduled-control-systems.html 

Gain Scheduling Basics: Gain scheduling is an approach to control of nonlinear systems using a family of linear controllers, each providing satisfactory 
control for a different operating point of the system. Gain-scheduled control is typically implemented using a controller whose gains are automatically 
adjusted as a function of scheduling variables that describe the current operating point.

We at TeK Associates are optimistic about the status of control theory in general and we are enthusiastic about:

	Bossert, D. E., Lamont, G. B., Horowitz, I., “Design of Discrete Robust Controllers using Quantitative Feedback Theory and a Pseudo-Continuous-Time Approach,” on pp. 25-31 in Osita D. T. NWOKAH (Ed.), Recent Developments in Quantitative Feedback Theory: Work by Prof. Issac Horowitz (predating research in Robust Control by two decades), presented at the winter annual meeting of the American Society of Mechanical Engineers,  Dallas, TX, 25-30 Nov. 1990;
	Barnard, R., “A Quantitative Feedback Theory Based on Time Domain and Fixed Point Notions (as a consequence of contraction mappings encountered),” on 45ff. in Osita D. T. NWOKAH (Ed.), Recent Developments in Quantitative Feedback Theory: Work by Prof. Issac Horowitz, presented at the winter annual meeting of the American Society of Mechanical Engineers,  Dallas, TX, 25-30 Nov. 1990;
	Intelligent Control and Adaptive Systems, Ed./Chair Guillermo Rodriguez, Proceedings of SPIE-The International Society for Optical Engineering, Vol. 1196, Bellingham, WA, 7-8 Nov. 1989;
	Butkovskiy, A. G., Pustyl'nikov, A. M., Mobile Control of Distributed Parameter Systems, Ellis Horwood Ltd., Chichester, Halstead Press, division of John Wiley, NY, 1997 (especially see Appendix 6 for 23 varieties of Integral Transforms on pp. 249-267; Appendix 7: Sobolev Transform; Appendix 12: On an Approximation Investigation of Mobile Control Problems for Distributed Control);
	Becedas, J., Mamani, G., Feliu, V., Siva-Ramirez, H., “Estimation of Mass-Spring-Damper System,” in Advances in Computational Algorithms and Data Analysis, S.-I. Ao, B. Kieger, S.-S. Chen (Eds.), Springer Science & Business Media, 2009;
	Schlacher, K., Irschik, H., Kugi, A., “Control of Nonlinear Beam Vibrations by Multiple Piezoelectric Layers,” pp. 355-362 in IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems, D. H. VanCampen (Ed.), Kluwer Academic Publishers, Netherlands, 1997;
	Hajek, O., Control Theory in the Plane, 2nd Edition, Lecture Notes in Control and Information Sciences, Springer-Verlag, NY, 2009;
	Ching, S.-N., Eun, Y., Gokcek, C., Kabamba, P. T., Meerkov, S. M., Quasilinear Control: Performance analysis and design of feedback systems with nonlinear sensors and actuators, Cambridge University Press, Cambridge, UK, 2011.

To complete the expose started above, recall the creatively designed endeavor below which featured a multiple model bank of N Kalman filters in parallel with an LQ feedback regulator control law for each Kalman filter equipped feedback branch after which the aggregated net result of the particular scalar weightings consisting of the individual probabilities, as calculated on-line in real-time, and corresponding to any particular branch of the LQG being correctly associated with the present mode (of only N different possible modes being modeled) for the actual multi-mode system under consideration:

Athans, M., Castanon, D., Dunn, K.-P., Lee, W. H., Sandell, N. R., Willsky, A. S., “The Stochastic Control of the F-8C Aircraft using a Multiple Model Adaptive Control (MMAC) method - I: Equilibrium Flight,” IEEE Trans. on Automatic Control, Vol. 22, No. 5, pp. 768-780, Oct. 1977. Was non-equilibrum flight ever considered or handled (where non-equilibrium flight is take-offs and landings and dog fight maneuvers or even maneuvers as benign as just coordinated turns)? Did this approach actually work? Was there ever a Phase II follow-on thus indicating success of the particular approach? The answer appears to be “no” on all three counts. This constitutes a high profile publicity stunt or charade without any useful payoff to the NASA customer. This was business as usual in some circles! I definitely would like to chase the money changers from the temple (of learning and useful knowledge). If they had not been pretending so hard that LQG theory was not fatally flawed, they could have equipped each LQG leg with a stable replacement LQG/Loop Transfer Recovery, as its correction. The resulting redesign may now actually work as they had hoped the initial version would.

Perhaps the funniest situation was when several people complained that the IEEE TAC paper review system was, perhaps, apparently being abused by reviewers or assistant editors being the first to see and then recognize a significant new result and then dispatch a graduate student (among an ample pool of available talent) to either use the topic of the paper under review as their thesis or write a paper on the topic themselves and then submit it for publication even before the original paper had appeared in print for the first time (a process that took about two years in those days). Afterwards, people at a particular institution would just reference the work of the authors affiliated with the same institution and ignore the true originator (who should have been acknowledged as having had the precedent) as yet another example of the "NIH" syndrome. What was funny was who was on the two man committee: Prof. Michael Athans and Prof. Y.-C. "Larry" Ho [one who almost always indulged in "NIH" behavior and the other who didn't and was known for his steadfast integrity, respectively] to look into the possible problem and who jointly reported their conclusions that everything regarding the current IEEE TAC review process was just fine! Isn't that particular situation like “having the fox guard the chicken coop?”

In the old days (1970's and, perhaps, before), in order for a Navy Sea Hawk SH-60 helicopter to land on a ship's deck during high winds and a corresponding "high sea state", it would drop a strong steel cable that would be attached to a winch aboard ship. Then the helicopter would pull up against the cable to make the cable taught as the winch reeled it in. In that way, the helicopter would perfectly match the ship's motion on roughest of seas as it landed. RAN MH-60 Helicopter RAST Recovery Assist Explained:
https://www.youtube.com/watch?v=6XvdXwgYN_s 

Years later (~1990's), I heard a presentation by (the late) Prof. Mike Athans at MIT (& Alphatech), where there was an attempt to do everything without the cable and, instead, rely only on a laser radar down and retroreflector-based back bounce control law for the landing. Even though I did not observe a cable in the above video, I still suspect that the complicated approach just described was not used here. The cable approach is robust and straight-forward. Judging by the way the helicopter moves perfectly to match the heaving of the ship's deck without any apparent computational delay (that would be incurred if a laser radar and a control law implementation were jointly used to control the helicopter's landing), I strongly suspect that there is a cable present. Modern cables can be made of carbon "Buckyballs" now for sufficient tensile strength without being easily visible to the naked eye. (At least it is something useful and a practical application for Buckyballs instead of a somewhat controversial (understatement) hypothesized "Space Elevator".
Click to view Japan's solution: https://www.youtube.com/watch?v=ZAjyBUnO9QY

One further example: I am not accusing all of MIT of practicing "NIH" but am only complaining about the inner workings of one particular department that I am very familiar with: Electronic Systems Laboratory (ESL), which changed its name to Laboratory for Information and Decision Systems (LIDS). My complaint is only for a particular time epoch from the late 1960's until some aspects of the present and does not include or apply to everybody working in this department, nor to the students who graduated from this department; but merely to the "trickster" at the top for many of those years [who was also a brilliant teacher and insightful researcher with extensive breath and depth and an ability to communicate ideas simply and clearly so that ALL could understand]. (My own [115] was based on some of his earlier work.) However, in the 1990's, he even told his graduate students in class (which I overheard, as an outside member of the audience) how he handled the following situation: "One of my prior students, who had already graduated and was now working in industry, in seeking to apply some aspect of my prior published technique to a particular application in seeking to apply my earlier results to but then, unfortunately, encountered a problem in taking it to fruition in the manner expected. This graduate, now in industry, successfully persuaded his supervisor to finance a consulting visit for me to help resolve the problem and help them get over the perceived temporary hurdle. While there on location, I sought a private audience with my prior student's supervisor from whom this employee, got that consulting assignment for me; I told his supervisor that he "was not the sharpest knife in the drawer"!" Again, “biting the hand that feeds him!” Paying back an act of kindness by throwing his former student "under the bus". Prof. Michael Athans' meaning was clear: "If you bother me with some theoretical aspect or "wrinkle" associated with the material of this course after you leave here, I will do the same thing to you!" Usually, subsequent consulting work on the same topics and material already known and conveyed in prior classes on the subject is viewed as an opportunity to be a hero and "save the day" for its industrial application! It's a pity that Prof. Athans, apparently, did not view it that way. Perhaps later in life, he was merely too busy and did not want to interrupt what he was working on at the time. I will remember the fun times (e.g., at several meetings of the CDC in New Orleans, as he crossed Canal Street, with an impish grin on his face, and as he proceeded down Bourbon Street with Sol Gully [https://www.linkedin.com/in/sol-gully-4779a326] to take in some of the many performances there). Prof. Athans had a very colorful personality. He will indeed be missed!

We at TeK Associates consider ourselves to have been extremely lucky for over more than forty years by our employers being in convenient proximity of two major educational institutions of higher learning where outstanding leaders in control theory taught; and who allowed us to attend important outside lecturers and presentations for free at both Harvard University (where Y. C. "Larry" Ho allowed us to hear but not ask questions nor make comments) and MIT (where we were allowed to ask probing questions). We also had library cards at both institutions, which greatly aided our research into these subjects. Weekly attendance at TASC "White Noise Hours" also provided us with experience more encompassing than our own mere first-person experience because we benefited from direct cross-corroboration with others who had different challenges. I also frequently used the Engineering and Science Library at Boston University, the Snell Library at Northeastern University, the Air Force Geophysical Library at Hanscom Field AFB (which became the Phillips Library) before it all moved to Albuquerque, New Mexico, the Lincoln Laboratory Library while I was working there, and the MITRE library in Bedford, MA (while I was consulting there) before it was dismantled in the early 2000's to be merely a "shadow of its former self".

Another variation of sorts of the dreaded NIH syndrome, discussed above, occurs in the following:

	Smith, S. T., “Statistical Resolution Limits and the Complexified Cramer-Rao Bound,” IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1597-1609, May 2005.
	Smith, S. T., “Covariance, Subspace, and Intrinsic Cramer-Rao Bounds,” IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1610-1630, May 2005.

where no reference is made to the following prior publication on this Cramer-Rao Lower Bound topic:

Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 5, pp. 590-601, September 1989 (Author’s reply in Vol. AES-26, No. 5, pp. 896-898, September 1990).

No there is not “a new sheriff in town” since THK III has pretty much been here and on station all along with eternal vigilance since 1971: “Making a list and checking it twice---trying to find out who’s naughty or nice....”

	Click here to view our recent short comment submitted to the Institute of Navigation for publication in their Journal. Kerr, T. H., “Comment on 'Low-Noise Linear Combination of Triple-Frequency Carrier Phase Measurements',” Navigation: Journal of the Institute of Navigation, Vol.57, No. 2, pp. 161,162, Summer 2010.
	Kerr, T. H., “Comment on ‘Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer’,”  AIAA Journal of Guidance, Control, and Dynamics, July-Aug. 2007.
	Kerr, T. H., “Comments on ‘Determining if Two Solid Ellipsoids Intersect’,” AIAA Journal of Guidance, Control, and Dynamics, January-February 2005.
	Kerr, T. H., “Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.
	Kerr, T. H., “Sensor Scheduling in Kalman Filters: Evaluating a Procedure for Varying Submarine Navaids,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.
	Kerr, T. H., “Vulnerability of Recent GPS Adaptive Antenna Processing (and all STAP\SLC) to Statistically Non-Stationary Jammer Threats,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001.
	Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001. (closed-form analytic solutions and IMM critique near the end)
	Kerr, T. H., “New Lamps for Old: a shell game for generalized likelihood ratio use in radar? Or this isn’t your father’s GLR!,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001.
	Kerr, T. H., “TeK Associates’ view in comparing use of a recursive Extended Kalman Filter (EKF) versus use of Batch Least Squares (BLS) algorithm for UEWR,” TeK Associates, Lexington, MA, (for Raytheon, Sudbury, MA), 12 Sep. 2000.
	Kerr, T. H., “Considerations in whether to use Marquardt Nonlinear Least Squares vs. Lambert Algorithm for NMD Cue Track Initiation (TI) Calculations,” TeK Associates Technical Report No. 2000-101, Lexington, MA, (for Raytheon, Sudbury, MA), 27 Sep. 2000.
	Kerr, T. H., “Critique of Some Neural Network Architectures and Claims for Control and Estimation,” IEEE Transactions on Aerospace and Electronic Systems, April 1998.
	Kerr, T. H., “Comments on ‘An Algorithm for Real-Time Failure Detection in Kalman Filters’,” IEEE Trans. on Automatic Control, May 1998.
	Kerr, T. H., “A Critical Perspective on Some Aspects of GPS Development and Use,” Proceedings of 16th Digital Avionics System Conference, Vol. II, pp. 9.4-9 to 9.4-20, Irvine, CA, 26-30 Oct. 1997.  [all worries expressed here by the author regarding GPS vulnerabilities were confirmed in experience in Three W. Mark Barnes, "Artillery Surveyors: Nomads of the Battlefield," Field Artillery, A Professional Bulletin for Redlegs, HQDA P B6-01-1, pp.43-47, Jan.-Feb. 2001]
	Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2D for Real-Time Multisensor Image Fusion and\or Restoration: Optimality of Some Decentralized KF Architectures,” Proceedings of the International Conference on Signal Processing Applications & Technology (ICSPAT96), 7-10 October 1996.
	Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proceedings of the International Conference on Signal Processing Applications & Technology (ICSPAT), 24-26 October 1995.
	Kerr, T. H., “Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” Institute of Navigation Proceedings of GPS-94, 20-23 Sept. 1994.
	Kerr, T. H., “Emulating Random Process Target Statistics (using MSF),” IEEE Transactions on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, April 1994. (closed-form analytic solutions and critique in Appendix)
	Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, March 1991.
	Kerr, T. H., “An Invalid Norm Appearing in Control and Estimation,” IEEE Transactions on Automatic Control, Vol. 23, No. 1, Feb. 1978.  (counterexamples and a correction)
	Kerr, T. H., “Testing Matrices for Definiteness and Application Examples that Spawn the Need,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, pp. 503-506, Sept.-Oct., 1987.
	Kerr, T. H., “Rationale for Monte-Carlo Simulator Design to Support Multichannel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test Cases,” MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 December 1989 (BSD).
	Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 5, pp. 590-601, Sep. 1989. (an expose)
	Kerr, T. H., “On Misstatements of the Test for Positive Semidefinite Matrices,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 571-572, May-Jun. 1990. (occurring in Nav & Target Tracking s/w in ‘70’s/’80's).
	Kerr, T. H., “Fallacies in Computational Testing of Matrix Positive Definiteness/Semidefiniteness,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, pp. 415-421, Mar. 1990. [Using counterexamples, he identifies fallacious algorithms that he found to exist in U.S. Navy submarine navigation and sonobuoy operational software that he reviewed in the late 1970's and early 1980's.]
	Kerr, T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control,” in Control and Dynamic Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in Algorithms and computational Techniques for Dynamic Control Systems, Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988.
	Kerr, T. H., “Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation Systems,” Proceedings of the National Technical Meeting of the Institute of Navigation (ION), San Diego, CA, 15-17 January 1985. (an expose)
	Kerr, T. H., “Decentralized Filtering and Redundancy Management for Multisensor Navigation,” IEEE Trans. on AES, Vol.23, No. 1, pp. 83-119, Jan. 1987. (an expose)
	Kerr, T. H., “Examining the Controversy Over the Acceptability of SPRT and GLR Techniques and Other Loose Ends in Failure Detection,” Proceedings of the American Control Conference, San Francisco, CA, 22-24 June 1983.  (an expose)
	Kerr, T. H., “Comments on ‘A Chi-Square Test for Fault Detection in Kalman Filters’,” IEEE Transactions on AC, Vol. 35, No. 11, pp. 1277-1278, November 1990.
	Kerr, T. H., “A Critique of Several Failure Detection Approaches for Navigation Systems,” IEEE Transactions on AC, Vol. 34, No. 7, pp. 791-792, July 1989.
	Kerr, T.H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C.T. Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.
	Kerr, T. H., “The Proper Computation of the Matrix Pseudo-Inverse and its Impact in MVRO Filtering,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 21, No. 5, Sep. 1985.
	Kerr, T. H., “The Principal Minor Test for Semidefinite Matrices-Author’s Reply,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, p. 767, Sep.-Oct. 1989.
	Kerr, T. H., “Three Important Matrix Inequalities Currently Impacting Control and Estimation Applications,” IEEE Transactions on Automatic Control, Vol. AC-23, No. 6, December 1978.
	Kerr, T. H., “Functional and Mathematical Structural Analysis of the Passive Tracking Algorithm (PTA),” Intermetrics Report No. IR-MA-208, Cambridge, MA, 25 May 1983, for NADC.
	Kerr, T. H., “Comments on ‘Estimation Using a Multirate Filter’,” IEEE Transactions on Automatic Control, Vol. AC-34, No. 3, p. 384, March 1989.
	Kerr, T. H., “Comments on ‘Federated Square Root Filter for Decentralized Parallel Processes’,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-27, No. 6, November 1991.   Go to Top

The close (equivalent) model relationship between a Box-Jenkins time-series representation and a state variable representation has been known for a least  4 or 5 decades, as spelled out in:  A. Gelb (Ed.), “Applied Optimal Estimation,” MIT Press, Cambridge, MA, 1974.

	Kerr, T. H., “Applying Stochastic Integral Equations to Solve a Particular Stochastic Modeling Problem,” Ph.D. Thesis in the Department of Electrical Engineering, University of Iowa, Iowa City, Iowa, January 1971. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)
	Kerr, T. H., Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral Factorization, MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 March 1989. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)
	Kerr, T. H., “Emulating Random Process Target Statistics (Using MSF),” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, Apr. 1994. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)

Go to Top

TeK Associates' Motto: "We work hard to make your job easier!"