Stability analysis of nonlinear systems via piecewise linear Lyapunov functions

This paper addresses the issue of constructing piecewise linear Lyapunov functions (PWLLF) for nonlinear systems satisfying the generalized sector condition, which is a generalization of the polytopic uncertainty. The main result of this paper is to propose a fast method to solving linear programming problems (LPs) which appear repeatedly in constructing PWLLF. The method uses a special structure of LPs which appear in constructing PWLLF.