The maximal contractively invariant ellipsoids for discrete-time linear systems under saturated linear feedback

In this paper, we consider the problem of determining the maximal contractively invariant ellipsoids for discrete-time linear systems with multiple inputs under saturated linear feedback. We propose an algebraic computational approach to determining such maximal contractively invariant ellipsoids. We divide the state space into several regions according to the saturation status of each input, and compute the possible maximal contractively invariant ellipsoids on each region except the region where none of inputs saturate and on their intersections. The minimal one among these possible maximal contractively invariant ellipsoids is the maximal contractively invariant ellipsoids of the system. Simulation results demonstrate the effectiveness of our methods.