Stability Analysis and Controller Design for a Class of Relay Control Systems

This note concerns stability analysis and controller design for a class of relay control systems. Based on full-order Luenberger observer and Lyapunov approach, the constructive sufficient conditions for the existence of the hyperplane-based switching law, which guarantees the stabilization of the closed-loop systems, are proposed. It is also shown that these conditions can be derived in terms of feasibility of a set of linear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of our methods.