A construction method of Lyapunov functions for piecewise-linear systems

The authors propose a Lyapunov-function construction method, giving the asymptotic stability region of a piecewise-linear (PWL) dynamical system. Lyapunov functions are constructed by connecting quadratic functions on each divided region, so that the computational tasks to obtain the asymptotic stability region are simplified. Also given is a simple condition according to which the asymptotic stability region of the PWL system is included in that of original nonlinear system.<>