Multiple-mode adaptive state estimator for nonlinear switched systems

Abstract

This paper deals with the issue of state estimator design for nonlinear switched systems. A multiplemode adaptive estimator is proposed under mode-dependent average dwell time (MDADT) switching, and the switching signal with MDADT constraint is also obtained to guarantee the exponential stability of estimation error dynamics, where the Lipschitz constant may be unknown since it is adaptively adjusted by designing an adaptation law. Based on both Lyapunov stable theory and the feasible solution of an optimization problem with linear matrix inequality constraint, the gain matrices and switching signals are provided, respectively. The sufficient conditions of the existence of multiple-mode adaptive switched estimator are also derived. Meanwhile, the above methods are also extended to the case of the average dwell time (ADT) switching, and an algorithm is given to summarize the implementation of the proposed estimators. Finally, the effectiveness of the designed methods is illustrated by simulation examples.