Observer design of piecewise discrete time linear systems

This paper presents a number of results on state estimation for piecewise discrete time linear systems based on a piecewise Lyapunov function. The major issue addressed in this paper is that the transitions of plant states and their estimates among regions of the state space may not be synchronized. It is shown that the proposed design approaches can guarantee the stability of the resulting state estimation error systems and the state estimator gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are finally given to illustrate the performance of the proposed approach.