Delay-dependent H∞ output feedback control for switched systems with time-delay
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KünyeNie, H., Zhao, J., Dimirovski, G. M., Li, P., Song, Z., & Liu, T. (2010). Delay-dependent H∞ output feedback control for switched systems with time-delay. In 2010 29th Chinese Control Conference (CCC) (pp. 938-943). Piscataway, NJ: IEEE.
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.