A novel H∞ tracking control scheme for periodic piecewise time-varying systems

In this work, a novel H-infinity tracking control scheme is designed for a class of periodic piecewise systems with time-varying subsystems. The reference model is a periodic piecewise linear system that allows the existence of unstable subsystems. Based on periodically time-varying Lyapunov functions, a sufficient condition is proposed to guarantee the exponential stability of augmented tracking system in the H-infinity sense. Taking advantage of the negative definiteness property of a type of matrix polynomials, an H-infinity state tracking controller with periodically time-varying gains is provided via a series of continuous matrix functions, which can be efficiently online computed by the solutions of straightforward convex optimization. Numerical simulations are presented to demonstrate the effectiveness of the proposed scheme. (C) 2019 Elsevier Inc. All rights reserved.