State Estimation and Sliding Mode Control of Uncertain Switched Hybrid Systems

This paper is concerned with the sliding mode control (SMC) design methodology for a class of uncertain switched hybrid systems with the unmeasurable states. A state observer is designed first, and then some conditions for the convergence of the estimated state error are obtained. By matrix transformation techniques, the solvability condition for the corresponding observer gain is established in terms of a set of linear matrix inequalities (LMIs). Based on the estimated states, a sliding surface is constructed, which guarantees the equivalent sliding motion restrict to the sliding surface under a designed switching law. A SMC law is then synthesized for the reaching motion such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approaches.