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Characterization of Stabilizing Switching Sequences in Switched Linear Systems Using ? Piecewise Linear Lyapunov Functions Xenofon D. Koutsoukos 1 and Panos J. Antsaklis 2 1 Xerox Palo Alto Research Center 3333 Coyote Hill Road, Palo Alto, CA 94304, USA koutsouk@ 2 Department of Electrical Engineering University of Notre Dame, Notre Dame, IN 46556, USA antsaklis.1@ Abstract. In this pap er, the stability of switched linear systems is inves- tigated using piecewise linear Lyapunov functions. Given a switched lin- ear system, we present a systematic metho dology for computing switch- ing laws that guarantee stability based on the matrices of the system. We assume that each individual subsystem is stable and admits a piece- wise linear Lyapunov function. Based on these Lyapunov functions, we comp ose \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 parti- tions of the state space. The approach is applied to b oth discrete-time and continuous-time switched linear systems. 1 Intro duction In this pap er, we study the stability of continuous and discrete-time switched linear systems using piecewise linear Lyapunov functions and we identify classes of switching sequences that result in stable trajectories. The main motivation b ehind this problem is that it is often easier to nd switching controllers than to nd a xed controller. In the case when we ha