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Structured and simultaneous Lyapunov functions for system stability problems. (English) Zbl 0729.93067
Robustness in identification and control, Proc. Int. Workshop, Turin/Italy 1988, 243-262 (1989).
Summary: [For the entire collection see Zbl 0723.00048.]
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of \(\dot x=Ax\) for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given. Proofs can be found in the authors [Int. J. Control 49, No.6, 2215-2240 (1989; Zbl 0683.93057)].

93D30 Lyapunov and storage functions