Analysis and controller design of discrete-time linear systems with state saturation

This paper studies the problem of stability analysis and controller design for discrete-time linear time invariant (LTI) systems with state saturation. Both full state saturation and partial state saturation are considered. Firstly, a new system model is constructed for solving the key problem. Then, a new method is presented for estimating the domain of attraction of the origin for a system with state saturation. Based on this method, an LMI-based ( linear matrix inequality) iterative algorithms is proposed for determining if a given ellipsoid is contractively invariant. Moreover, an LMI-based algorithm is developed for designing dynamic output-feedback controllers which guarantee that the domain of attraction of the origin for the closed-loop system is as large as possible. An example is given to illustrate the efficiency of the design method.