Switching systems with dwell time: Computing the maximal Lyapunov exponent. (May 2021)

• Record Type: Journal Article
• Authors: Chitour, Yacine; Guglielmi, Nicola; Protasov, Vladimir Yu.; Sigalotti, Mario
• Is Part Of: Nonlinear analysis. Volume 40(2021)
• Publication Date: 2021-05
• Subjects: 37B25 -- 37M25 -- 15A60 -- 15-04; Switching systems -- Dwell time -- Lyapunov exponent -- Polytopic Lyapunov function -- Constrained switching -- Invariant polytope algorithm; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2021.101021
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete–continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions. Each discrete action has its own positive weight which accounts for its time-duration. We develop a theory of stability for the mixed systems; in particular, we prove the existence of an invariant Lyapunov norm for mixed systems on graphs and study its structure in various cases, including discrete-time systems for which discrete actions have inhomogeneous time durations. This allows us to adapt recent methods for the joint spectral radius computation (Gripenberg's algorithm and the Invariant Polytope Algorithm) to compute the Lyapunov exponent of mixed systems on graphs.