When is a set of LMIs a sufficient condition for stability?

Amir Ali Ahmadi, Raphael M. Jungers, Pablo A. Parrilo, Mardavij Roozbehani

We study stability criteria for discrete time switching systems. We investigate the structure of sets of LMIs that are a sufficient condition for stability (i.e., such that any switching system which satisfies these LMIs is stable). We provide an exact characterization of these sets. As a corollary, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies the stability of a switching system.

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