Robust H∞ tracking control design for a class of switched linear systems using descriptor redundancy approach

In this paper, the design of a switched Proportional-Derivative (PD) controller, for a class of Switched Linear Systems (SLS) subject to external disturbances, is investigated for the purpose of satisfying the robust H_∞ output feedback tracking performance. The main idea of the proposed synthesis approach consists to use the descriptor redundancy formulation in order to decouple the crossing terms between the controller´s and the switched system´s matrices. Based on the multiple Lyapunov functional methods, sufficient conditions for the existence of a switched PD controller are formulated in terms of Linear Matrix Inequalities (LMI). The efficiency of the proposed synthesis procedure is illustrated by a numerical example.