Set-Membership Interval State Estimator Design Using Observability Matrix for Discrete-Time Switched Linear Systems

Abstract

The main goal of this paper is to present a new approach to set-membership interval state estimator design for the uncertain discrete-time switched linear systems (SLS). The upper and lower estimation errors are measured a-priori under the assumption that the uncertainties are unknown but bounded. The observability matrix and the set-inversion of the available system outputs are used to solve the interval based state estimation problem under arbitrary switching sequence. The boundedness of the estimation error dynamics is proved without the observer gain. Moreover, it is shown that the width of the estimated state vector converges to a known value within finite time, that significantly improves the accuracy of the proposed approach. Finally, the effectiveness of the proposed technique is demonstrated through numerical simulations.