Structured singular values and invariant theory
Structured singular values are functions defined on the set of n × n matrices. They describe, in some sense, how close a matrix is to zero. Special cases are the spectral radius function and the operator norm function. Such functions are used in control engineering as a mathematical tool for robustness analysis of feedback control systems, when the physical plant (vehicle, process, etc.) is subject to parametric uncertainty. In particular, structured singular values have been used by Honeywell to analyze the robustness of the descent flight-control system of the Space Shuttle; they are also being used in flight-control design and analysis for the NASP and other aerospace vehicles currently in the design phase.
KeywordsParametric Uncertainty Invariant Theory Projective Variety Robust Stability Space Shuttle
Unable to display preview. Download preview PDF.
- B. Morton and R. McAfoos, A Mu-Test for Robustness Analysis of a Real-Parameter Variation Problem, 1985 American Control Conferences Proceedings, Boston.Google Scholar
- B. Morton, New Applications of Mu to Real-Parameter Variation Problems, 1985 Conference on Decision and Control Proceedings, Ft. Lauderdale.Google Scholar
- G. Salmon, Higher Algebra, Fifth Edition, Reprint from Text Originally Published in 1885, Chelsea, New York.Google Scholar
- W.V.D. Hodge and D. Pedoe, Methods of Algebraic Geometry, Cambridge University Press, 1968.Google Scholar
- A. Packard and J.C. Doyle, Robust Control of Multivariable and Large Scale Systems, Honeywell Final Report on Contract No. F49620–86-C-0001 to AFOSR, for work during period October 1985 through March 1988.Google Scholar