Robust H∞ State Observer Design for a Class of Linear Time-Delay Systems via Switching

This paper addresses the problem of robust H_infin observer design for a class of linear time-delay systems. Suppose that there exist finite candidate observers in a given set of observers, none of which is a robust H_infin state observer, and the gain matrices of state observers are all given or all unknown. This paper designs a switching law between observers such that the error system is stabilizable with an H_infin-norm bound. Based on single Lyapunov function technique and multiple Lyapunov function technique, respectively, two sufficient conditions for switched error systems to be stabilizable with an H_infin-norm bound are derived and the suitable observer gain matrices are given when they are unknown. The results provide a new insight into the synthesis problems of observer-based H_infin controller. All results are given by linear matrix inequalities (LMIs). Finally, a simulation example illustrates the validity and applicability of the present approach