Abstract

This paper addresses stability analysis of closed-loop sampled-datapiecewiseaffine (PWA) slabsystems. 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-datasystem 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 asymptoticstability of sampled-data PWA slabsystems 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 asymptoticstability. Therefore, the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptoticstability of the sampleddatasystem. The new results are successfully applied to a unicycle example.