Variable Structure Control With Generalized Relays: A Simple Convex Optimization Approach

The article proposes a convex optimization approach for the design of relay feedback controllers. The case of linear systems is studied in the presence of matched perturbations. The system input is a generalized relay that may take values in a finite set of constant vectors. A simple design method is proposed using linear matrix inequalities (LMIs). Furthermore, the approach is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid of the order of the sampling interval. Time-varying uncertainties (in the state matrix and the sampling interval) can be easily included in the analysis.