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Non-Euclidean metrics and the robust stabilization of systems with parameter uncertainty. (English) Zbl 0592.93044
Authors’ abstract: ”This paper considers, from a complex function theoretic point of view, certain kinds of robust synthesis problems. In particular, we use a certain kind of metric on the disk (the ”hyperbolic” metric) which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non-Euclidean geometry. It is shown that several apparently different problems can be treated in a unified general framework. A new result on the gain margin problem for multivariable plants is also given. Finally, we apply our methods to systems with real zero or pole variation.”
The present paper is a nice application of certain basic methods of classical complex analysis. Old ideas of R. Nevanlinna and G. Pick are employed here to get new results in systems theory.
Reviewer: M.Seppälä

MSC:
93D15 Stabilization of systems by feedback
30E99 Miscellaneous topics of analysis in the complex plane
93B35 Sensitivity (robustness)
30E05 Moment problems and interpolation problems in the complex plane
93B50 Synthesis problems
93C35 Multivariable systems, multidimensional control systems
93D20 Asymptotic stability in control theory
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