Abstract
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.
Original language | English (US) |
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Article number | 7858590 |
Pages (from-to) | 3062-3067 |
Number of pages | 6 |
Journal | IEEE Transactions on Automatic Control |
Volume | 62 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2017 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering
Keywords
- Linear matrix inequalities
- lyapunov methods
- set theory
- stability
- switching systems (control)