## 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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