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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:
93D05Lyapunov and other classical stabilities of control systems
34D20Stability of ODE
90C90Applications of mathematical programming
93C05Linear control systems