Decay rates for stabilization of linear continuous-time systems with random switching

Fritz Colonius (1) , Guilherme Mazanti (2)

1 Institut für Mathematik [Augsburg]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time.

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

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

Fritz Colonius, Guilherme Mazanti. Decay rates for stabilization of linear continuous-time systems with random switching. Mathematical Control and Related Fields, 2019, 9 (1), pp.39-58. ⟨10.3934/mcrf.2019002⟩. ⟨hal-01232164v3⟩