Active Mode Identification and Continuous State Estimation for Switched Linear Systems with Unknown Inputs and Slow Switching Signal

This paper addresses the issue of state observation for a switched linear system with unknown inputs and slow switching signal when the current mode (active mode) of the switched system is unknown. First, both state and output transformations are considered to deal with the unknown inputs of the switched system, and a reduced-order switched system that eliminates the effects of unknown inputs is constructed. Second, for each reduced-order subsystem, a corresponding observer is designed, and multi-observers for the reduced-order switched system are developed. Next, a kind of active mode identification method is proposed by minimizing the output residual norms that are derived from multi-observers. Third, based on the identified active mode, the continuous state estimation of the original switched system is approximately realized. Finally, a simulation example is given to illustrate the effectiveness of the proposed methods.