Design of Stabilizing Switching Control Laws for Discrete- and Continuous-Time Linear Systems Using Piecewise-Linear Lyapunov Functions

X.D. Koutsoukos and P.J. Antsaklis

International Journal Control, 75(12), 932-945, 2002.

Abstract -- In this paper, the stability of switched linear systems is investigated using piecewise linear Lyapunov functions. In particular, 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 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.

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