Some results on the stabilization of switched systems

Authors:
José Luis Mancilla-Aguilar;Rafael Antonio GarcíA
Affiliations:
-;-
Venue:
Automatica (Journal of IFAC)
Year:
2013

Citing 6
Cited 0

Introduction to Hybrid Dynamical Systems

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Feedback Stabilization and Lyapunov Functions

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Weak Converse Lyapunov Theorems and Control-Lyapunov Functions

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Stability Criteria for Switched and Hybrid Systems

SIAM Review
Asymptotic Controllability by Means of Eventually Periodic Switching Rules

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Optimal control of switching systems

Automatica (Journal of IFAC)

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Abstract

This paper deals with the stabilization of switched systems with respect to (w.r.t.) compact sets. We show that the switched system is stabilizable w.r.t. a compact set by means of a family of switched signals if and only if a certain control affine system whose admissible controls take values in a polytope is asymptotically controllable to that set. In addition we present a control algorithm that based on a family of open-loop controls which stabilizes the aforementioned control system, a model of the system and the states of the switched system, generates switching signals which stabilize the switched system in a practical sense. We also give results about the convergence and the robustness of the algorithm.