When is a set of LMIs a sufficient condition for stability?
Amir Ali Ahmadi, Raphael M. Jungers, Pablo A. Parrilo, Mardavij, Roozbehani
TL;DR
This paper characterizes the structure of sets of linear matrix inequalities (LMIs) that guarantee the stability of discrete-time switching systems, revealing the computational complexity of recognizing such sets.
Contribution
It provides an exact characterization of LMI sets that are sufficient for stability and proves the PSPACE-completeness of recognizing these sets.
Findings
Exact characterization of LMI sets guaranteeing stability
Recognition of such LMI sets is PSPACE-complete
Insights into the structure of stability conditions for switching systems
Abstract
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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