Stability analysis of uncertain piecewise linear systems using Piecewise Quadratic Lyapunov Functions

Piecewise Quadratic Lyapunov Functions (PQLFs) was proposed by Johansson and Rantzer in 1997. They mainly applied it to analyze stability of piecewise linear systems. It seems that they do not much attention to apply it for stability analysis of uncertain piecewise linear systems. The main objective of this paper is to propose a new stability criteria which is less conservative than the stability criteria proposed in the paper by Johansson and Rantzer. Moreover, we propose algorithms to examine conditions of proposing stability criteria. Some examples will be shown to demonstrate the usefulness of the proposing method.