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

Abstract

In this work, a novel H∞ 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∞ sense. Taking advantage of the negative definiteness property of a type of matrix polynomials, an H∞ 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.