Robust switched control based on strictly positive real systems and variable structure control techniques

Abstract

This paper is concerned with the design of variable structure controllers for uncertain switched linear plants. The proposed method is based on Lyapunov–Metzler inequalities and on properties of strictly positive real (SPR) systems, with the advantage that it can be applied in control of uncertain switched linear system. The first contribution shows that there exists a solution of the SPR synthesis for a class of linear uncertain switched systems using switched static output feedback, if and only if there exists a solution of this SPR synthesis with switched static state feedback. This result is a generalization of known conditions regarding this problem, for linear time-invariant and known (without uncertainties) plants, and offers a possible procedure for output feedback SPR synthesis: first solve the state feedback SPR synthesis and then, using the obtained solution, find a solution for the output feedback SPR synthesis. Next are presented necessary and sufficient (sufficient) conditions for the SPR synthesis for a class of linear uncertain switched systems using switched static output feedback, for plants with the same number of inputs and outputs (with the number of outputs greater than the number of inputs). Two examples illustrate the effectiveness of the robust control system, including applications of the proposed methods, considering switched static state feedback and switched static output feedback, in the design of switching control strategies for active suspensions systems in road vehicles. Performance indices such as decay rate, guaranteed cost, and restriction in the norm of controller gains are considered in these designs. Copyright © 2016 John Wiley & Sons, Ltd.