Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems

Abstract

The calculation of piecewise quadratic (PWQ) Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI) approach proposed in Johansson and Rantzer (1998) for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL) benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.