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An LMI approach to multi-model estimation for discrete-time linear systems

An approach to multi-model estimation for discrete-time linear systems is proposed that is based on the idea of using a bank of parallel observers. Stability issues have been considered and conditions have been found to ensure the convergence of the resulting error dynamics. In addition, such conditions guarantee the existence of an upper bound to a quadratic cost function of the estimation error. The observer gains may be selected by solving a set of linear matrix inequalities (LMIs). A method is described to design such observers that aims to optimize the performance. Moreover, such a design may be efficiently accomplished by using an LMI algorithm. Preliminary simulation results are reported to show the effectiveness of the proposed method.