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Abstract:
The first part of my talk is to present a methodology to design interval observers for discrete-time linear switched systems affected by bounded, but unknown disturbances. Two design techniques are presented. The fi rst one requires that the observation error dynamics are nonnegative while the second one relaxes this restrictive requirement by a change of coordinates. Furthermore, ideas of using $H_\infty$ formalism to compute optimal gains are proposed. The second part is to design interval observers for continuous nonlinear switched systems. The nonlinear modes are described by the multimodel approach of Takagi-Sugeno (T-S) fuzzy systems where premise variables depending on the state vector which is unmeasurable. We propose T-S interval observers that consider the unmeasurable premise variables as bounded uncertainties under common assumptions that additive disturbances as well as measurement noises are unknown but bounded. The stability and the nonnegativity conditions are given in terms of Linear Matrix Inequality (LMI) to ensure simultaneously the convergence and the nonnegativity of error dynamics. As in the first part, in the absence of measurement noises, we compute optimal gains which attenuate the effect of additive disturbances using $H_\infty$ approach to improve the accuracy of the present interval observers. Theoretical results are finally applied to numerical examples to highlight the performance of the introduced methods in both parts.