Hybrid observer design for linear switched system via Differential Petri Nets

The aim of this paper is to propose a hybrid observer design for linear switched systems modelled either via Differential Petri Nets (DPN) or via Timed Differential Petri Nets (TDPN). The switched systems, herein, considered are characterized by switching laws that can depend on the continuous states or on both of a given dwell time and the continuous states. In addition, the structure of the proposed observers is based on a discrete observer and a continuous observer on interaction. The discrete observer reconstructs the discrete mode, by estimating both of the discrete marking and the firing vector. Once, the active mode is obtained, the continuous states are estimated. Finally, the outputs of the continuous observer are used to update the marking and the firing vector. At the end of the paper, several simulation results are presented to illustrate the proposed approach.