Observer Design for Switched Systems using Multiple Quadratic Lyapunov Functions

In this paper, a state estimation approach of switched linear systems is proposed, resulting in a switched observer including state jumps. The observer synthesis problem, guaranteeing (exponentially) estimation error convergence, is formulated as a linear matrix inequality (LMI) problem. By using multiple Lyapunov functions, one for each observer mode, a switched state jump observer is designed for a broader class of switched systems than earlier proposed in the literature. By abruptly changing the estimator state at instants when the switched system changes mode, the estimation error will converge much faster than in earlier approaches