Delay-dependent H∞ output feedback control for switched systems with time-delay

The problem of H_∞ observer-based output feedback control for a class of switched systems with time-delay is addressed. By using a new state transformation, a delay-dependent sufficient condition for the problem to be solvable is given in terms of linear matrix inequalities. We show that when all subsystems have H_∞ observer-based output feedback controllers satisfying the LMIs, the switched system has a switching H_∞ observer-based output feedback controller. The key idea is to establish a new type of common Lyapunov function for all subsystems and the main feature is that a transformed subsystem is an equivalent descriptor subsystem to the observer-based feedback closed-loop subsystem. Furthermore, we extend these results to switched systems with multi-delay in the dynamics and in the objective function. A simulation example is presented to illustrate the validity of the results.