Robust Full Order and Reduced Order Observers for a Class of Uncertain Switched Systems

Abstract

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust slidingmode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reducedorder switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reducedorder switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a fullorder switched observer exists also guarantee the existence of a reducedorder switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified threetank system.