Robust Variable Structure Control for Uncertain Interconnected Systems Based on LMIs Approach

The problem of decentralized control was investigated for a class of mismatched uncertainties interconnected systems. Based on linear matrix inequalities approach, a sufficient condition of existing a group of linear sliding surfaces was given for uncertainties interconnected systems, and the variable structure controllers were designed. The controllers can guarantee that the state trajectory is directed towards to the linear sliding surfaces, sliding mode exists and the closed-loop systems are globe asymptotically stable. The design approach of controllers is simple, and the formation of the sliding surface is explicit. Finally, a simulation on the model of two inverted pendulums illustrates the proposed design approach