Stability analysis of discontinuous nonlinear systems via piecewise linear Lyapunov functions

The purpose of this paper is to present a stability analysis of discontinuous nonlinear systems using piecewise linear Lyapunov functions (PWLLF). The functions are parametrized by hyperplanes, which intersect the stability region, and stability conditions are formulated as linear programming problems (LP) in terms of the parameters inserted by the hyperplanes. An interesting feature of the analysis is that it can include the uncertainty caused by time delays which are inherent in switching devices controlling the system. A few examples are used to illustrate the obtained results