A Switch Controller Design for Linear Systems with Input Saturation Based on Nested Invariant Ellipsoids

A design method of switch controller is proposed for linear systems with input saturation. The key idea of switch controller is that, in each switching region, a local linear controller is selected such that the constraints imposed by saturation are not violated. Here a sequence of linear quadratic (LQ) controllers is pre-computed as local linear controllers. And for each local LQ controller, a corresponding positive invariant admissive ellipsoid (PIAE) is considered as switching region. Note that for a local linear controller a PIAE is a positive invariant ellipsoid in state space, which can avoid saturation occurring. Furthermore, the method is extended to linear time varying systems with polytopic uncertainty. Asymptotic stability for linear time invariant (LTI) systems and robust quadratic stability for polytopic systems are established. Finally two examples are illustrated and simulation results show the efficiency of the proposed method