Observer design for switching nonlinear systems

Abstract—In this paper we consider observer design for discrete-time switching systems represented by Takagi-Sugeno fuzzy models. For the design we use a switching Lyapunov function defined on the switches. In order to develop stability conditions for the estimation error dynamics, we consider the variation of this function along possible switches. The conser-vativeness of the approach is reduced by considering the α-sample variation of the Lyapunov function. This approach can bring solutions to observer design for some switching systems with unobservable and unstable local models. The developed conditions are illustrated on a numerical example. Index Terms—switching systems, Takagi-Sugeno fuzzy mod-els, observer design, periodic systems, nonquadratic Lyapunov function I