H-infinity control of switched linear parabolic systems

The $H_{\infty}$ control problem of a class of switched linear parabolic systems is considered. By applying the multiple Lyapunov function method and the average dwell time scheme, sufficient conditions for exponential stability and the $H_{\infty}$ control synthesis are established in terms of LMIs and a family of switching signals. The advantage in this work lies in the fact that sufficient conditions completely depend on the system parameters and the system can be analyzed by using numerical softwares. At the end of the paper, an example is given to illustrate the obtained result.