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Summary: STABILIZING SUPERVISORY CONTROL OF HYBRID
SYSTEMS BASED ON PIECEWISE LINEAR
LYAPUNOV FUNCTIONS1
XENOFON D. KOUTSOUKOS and PANOS J. ANTSAKLIS
Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556,
USA, xkoutsou,antsaklis.1@nd.edu
Abstract. In this paper, the stability of discrete-time piecewise linear hybrid systems is in-
vestigated using piecewise linear Lyapunov functions. In particular, we consider switched
discrete-time linear systems and we identify classes of switching sequences that result in
stable trajectories. Given a switched linear system, we present a systematic methodology for
computing switching laws that guarantee stability based on the matrices of the system. In the
proposed approach, we assume that each individual subsystem is stable and admits a piece-
wise linear Lyapunov function. Based on these Lyapunov functions, we compose "global"
Lyapunov functions that guarantee stability of the switched linear system. A large class of
stabilizing switching sequences for switched linear systems is characterized by computing
conic partitions of the state space.
Key Words. Stability, switched linear systems, piecewise linear Lyapunov functions, parti-
tions of the state space.
1. INTRODUCTION
In this paper, we study the stability of piecewise linear
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