Sampled-data control based on the observer for linear hybrid systems

In this paper, a H-infinity sampled-data control problem based on the observer for linear hybrid systems is presented. The hybrid system is mapped to the continuous-time domain and modeled as an augmented continuous one, where the control input and the measurement output have piecewise-continuous delays. A sufficient condition is derived to guarantee the closed-loop system is asymptotically stable and has a H_∞ performance level γ via Lyapunov-krasovskii functional method. The singular value decomposition approach is extended to resolve the nonlinear terms of the condition and the control problem is solved in forms of linear matrix inequalities. This approach gives a good solution to the unpredictable state problem in sampled-data control. A numerical example is given to demonstrate the validity of the proposed approach.