Asymptotic stability of piecewise affine systems with sampled-data piecewise linear controllers

Abstract

This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) systems. In particular, we study the case in which a PWA plant is in feedback with a sampled-data piecewise linear (PWL) controller. We consider the sampled-data system as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov-Krasovskii functional (LKF) for studying PWA systems with time delay. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of PWA systems in feedback with sampled-data PWL controllers. Finally, following the time-delay approach, we formulate the problem of finding a lower bound on the maximum delay that preserves asymptotic stability to the origin as an optimization program in terms of LMIs. The new results are successfully applied to a unicycle example.