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.
@article{arxiv.1201.3227,
title = {When is a set of LMIs a sufficient condition for stability?},
author = {Amir Ali Ahmadi and Raphael M. Jungers and Pablo A. Parrilo and Mardavij Roozbehani},
journal= {arXiv preprint arXiv:1201.3227},
year = {2012}
}