Asymptotic stability of sampled-data piecewise affine slab systems

This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) slab systems. In particular, we study the case in which a PWA plant is in feedback with a discrete-time emulation of a PWA 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 delays that is less conservative when compared to previously suggested alternatives. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of sampled-data PWA slab systems to the origin. These conditions become Linear Matrix Inequalities (LMIs) in the case of a piecewise linear (PWL) controller. Finally, we present an algorithm for finding a lower bound on the maximum delay that preserves asymptotic stability. Therefore, the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptotic stability of the sampled data system. The new results are successfully applied to a unicycle example.