Switching observer design for uncertain nonlinear systems

The problem of designing a switching observer for a finite or infinite set of nonlinear time-varying systems with unknown parameters and/or different structure is studied in this paper. Under a compactness condition on the set of the systems and a Lyapunov observability assumption proposed in this paper, it is shown an observer with switching dynamics can be constructed such that the overall error dynamics is asymptotically stable. Different from general variable structure method in observer design, only a finite number of switches occurs before asymptotically stability is achieved. The Lyapunov direct method is used to construct both switching gain and switching index. A special case of quadratic observability where the error dynamics becomes exponentially convergent is also provided to illustrate the observer design procedure