101. On the Joint Spectral Radius of Shuffled Switched Linear Systems
- Author
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Aazan, Georges, Girard, Antoine, Greco, Luca, Mason, Paolo, Laboratoire Méthodes Formelles (LMF), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)
- Subjects
Lyapunov Functions ,Switched Systems ,[INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY] ,Formal Languages and Automata ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Exponential Stability ,[SPI.AUTO]Engineering Sciences [physics]/Automatic - Abstract
International audience; We present and develop tools to analyze stability properties of discrete-time switched linear systems driven by shuffled switching signals. A switching signal is said to be shuffled if all modes of the system are activated infinitely often. We establish a notion of joint spectral radius related to these systems: the shuffled joint spectral radius (SJSR) which intuitively measures the impact of shuffling on the decay rate of the system's state. We show how this quantity relates to stability properties of such systems. Specifically, from the SJSR, we can build a lower bound on the minimal shuffling rate in order to stabilize an unstable system. Then, we present several methods to approximate the SJSR, mainly by computing lower and upper bounds using Lyapunov methods and some automata theoretic techniques.
- Published
- 2022