Asynchronous observer-based H∞ control for switched stochastic systems with mixed delays under quantization and packet dropouts

In this paper, the observer-based H∞ control problem is investigated for a class of discrete-time switched stochastic systems with mixed delays comprising both discrete and distributed delays. The measurement output of the addressed system is subject to quantizations and packet dropouts. The observer/controller switching is allowed to be asynchronous with the subsystem switching. An observer-based controller is designed such that, in the simultaneous presence of system switches, mixed delays, quantizations and packet dropouts, the closed-loop system is guaranteed to be mean-square exponentially stable while achieving the prescribed H∞ performance constraints. Based on the piecewise Lyapunov-like functionals and the average dwell-time switching, sufficient conditions are first established under which the closed-loop system is mean-square exponentially stable with a weighted disturbance attenuation level. Then, the explicit characterizations of the observer/controller gains are obtained by means of certain nonlinear matrix inequalities that can be effectively solved by applying the cone complementary linearization algorithm. Finally, a numerical example is given to show the effectiveness of the proposed design scheme.