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 conservativeness 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.

Limiting State Estimation of Switched Interval Systems with Metzler-Takagi-Sugeno Models

“…The same principal questions arising above are combined in the case of control design for T-S fuzzy switched systems [17], [18], [19], [20], [21] and in the technique of interval observers for switched T-S fuzzy systems [22], where positiveness becomes more relevant. It has to be underlined that pervasive deployments of these approaches have constituted an important base platform in controller and interval observer design for uncertain switched T-S fuzzy systems.…”

“…32-39 The feasible solution of ( 67 . Having in mind (22) it is not hard to verify that the condition A σ ei ≤ A σ ei is satisfied for all i = 1, 2, σ = 1, 2. Note, the small complexity of the LMI algorithmic problems and LMIs feasibility can be checked also when programming the task using the LMI toolbox of MATLAB © .…”

A note on observers design for one-sided Lipschitz nonlinear systems

“…For more specialized work, which consist of results on observers for sampled-data nonlinear systems [10], discrete-time sliding mode observers [12], discrete-time nonlinear systems [13], observers for Lipschitz nonlinear systems [8,13,14,16], and Lipschitz nonlinear discrete-time systems with time-delay [15]. Observer design for nonlinear systems with unknown inputs [17][18][19][20], switching nonlinear systems [21], one-sided Lipschitz nonlinear systems [22,23], and so on.…”