LMI design of a switched observer with model uncertainty: Application to a hysteresis mechanical system

In this paper, a linear matrix inequality (LMI) technique for observer based state estimation of discrete time linear switched systems with uncertainties is developed. Sufficient conditions of global convergence of the observer are proposed. The proposed observer design method is applied to estimate the states of a real continuous non-linear system with hysteresis. First, the non-linearities are divided in linear sub-models, second the system is discretized to give finally a discrete time linear switched model on which the proposed observer is applied. Simulation results are given to show the effectiveness of the proposed observer.