Luenberger Observers For Switching Discrete-Time Linear Systems

State estimation using Luenberger-like observers is considered for a class of switching discrete-time linear systems. The switching is assumed to be unknown among the various system modes described by known matrices. The convergence of the error dynamics is ensured, even in the presence of bounded noises, by conditions that can be expressed by means of Linear Matrix Inequalities (LMIs). The design of such observer may be accomplished by minimizing an upper bound on a quadratic cost function of the estimation error using LMI-based optimization techniques. Moreover, an improvement to the estimator is presented that is based on a projection technique.