A Characterization of Lyapunov Inequalities for Stability of Switched Systems
Author(s)Jungers, Raphael M.b.; Ahmadi, Amir A; Parrilo, Pablo A.; Roozbehani, Mardavij
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We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a sufficient condition for stability. Various such conditions have been proposed in the literature in the past 15 years. We prove in this note that a family of language-theoretic conditions recently provided by the authors encapsulates all the possible LMI conditions, thus putting a conclusion to this research effort. As a corollary, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies stability of a switched system. Finally, we provide a geometric interpretation of these conditions, in terms of existence of an invariant set.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers (IEEE)
Junger, Raphael M., Amirali Ahmadi, Pablo Parrilo, and Mardavij Roozbehani. "A Characterization of Lyapunov Inequalities for Stability of Switched Systems." IEEE Transactions on Automatic Control, Volume 62, Issue 6 (June 2017): pp. 3062-3067.