Optimal Interval Observer for Switched Takagi–Sugeno Systems: An Application to Interval Fault Estimation

The main goal of this article 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 that is unmeasurable. In this article, 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 to ensure simultaneously the convergence and the nonnegativity of error dynamics. Furthermore, in the absence of measurement noises, optimal gains attenuating the effect of additive disturbances are computed using H
_∞
approach to improve the accuracy of the present interval observers. Theoretical results are finally applied to a numerical example to highlight the performance of the proposed method.