Non-Euclidian metrics and the robust stabilization of systems with parameter uncertainty

1985/10/01 by P. Khargonekar, Pramod P. Khargonekar, A. Tannenbaum +1 · 1 citation
Physics and Astronomy · Mathematics · Engineering · #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems #Stability and Controllability of Differential Equations

paper · doi:10.1109/tac.1985.1103805

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-Euclidian 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 variations.

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