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Sampled-Data Control of LTI Systems with Relays: A Convex Optimization Approach

We consider a generalized class of relay controllers where the system input may take values in a finite set of constant vectors. A simple continuous-time design method is proposed for linear time invariant (LTI) systems. Furthermore, it is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid containing the origin. The sampling intervals may be unknown and time-varying in a given interval. Simple linear matrix inequalities (LMIs) conditions are proposed for checking (local) practical stability.