When is a set of LMIs a sufficient condition for stability?
  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. 
Amir Ali Ahmadi, Raphael M. Jungers, Pablo A. Parrilo, Mardavij   Roozbehani
math.OC cs.SY