Characterization of Stabilizing Switching Sequences in Switched
Linear Systems Using Piecewise Linear Lyapunov Functions
X.D. Koutsoukos and P.J. Antsaklis
Hybrid Systems: Computation and Control (HSCC 2001),
M. Di Benedetto and A. Sangiovanni-Vincentelli Eds.,
Vol. 2034, Lecture Notes in Computer Science, pp. 347-360,
Abstract -- In this paper, the stability of switched linear systems is
investigated using piecewise linear Lyapunov functions.
Given a switched linear system, we present a
systematic methodology for computing switching laws that guarantee
stability based on the matrices of the system.
We assume that each individual subsystem is stable
and admits a piecewise 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. The approach is applied to both discrete-time
and continuous-time switched linear systems.