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Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices. (English) Zbl 0810.93051
Summary: We establish a set of new necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices. We relate the above results to the existence of quadratic Lyapunov functions for linear time- invariant systems with interval-valued coefficient matrices. Then, we develop an algorithm to determine the Hurwitz and the Schur stability properties of interval matrices. We demonstrate the applicability of our results by means of two specific examples.

MSC:
93D09Robust stability of control systems
93C05Linear control systems
93D30Scalar and vector Lyapunov functions
93B40Computational methods in systems theory