Lyapunov exponents for random continuous-time switched systems and stabilizability

Fritz Colonius (1) , Guilherme Mazanti (2, 3)

1 Institut für Mathematik [Augsburg]
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 GECO - Geometric Control Design

For linear systems in continuous time with random switching, the Lyapunov exponents are characterized using the Multiplicative Ergodic Theorem for an associated system in discrete time. An application to control systems shows that here a controllability condition implies that arbitrary exponential decay rates for almost sure stabilization can be obtained.

Mots clés: random switching; Lyapunov exponents; Multiplicative Ergodic Theorem; almost sure stabilization; arbitrary rate of convergence

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Fritz Colonius, Guilherme Mazanti. Lyapunov exponents for random continuous-time switched systems and stabilizability. 2015. ⟨hal-01232164v1⟩