Investigating duality on stability conditions.(English)Zbl 1157.93457

Summary: This paper is devoted to investigate the role played by duality in stability analysis of linear time-invariant systems. We seek for a dual statement of a recently developed method for generating stability conditions, which combines Lyapunov stability theory with Finsler’s Lemma. This method, developed in the time domain, is able to generate a set of (primal) equivalent stability tests involving extra multipliers. The resulting tests have very attractive properties. Stability is characterized via linear matrix inequalities and we use optimization theory to obtain the duals. The dual problems are given a frequency domain interpretation.

MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 34D20 Stability of solutions to ordinary differential equations 90C90 Applications of mathematical programming 93C05 Linear systems in control theory
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