Stability and Stabilization Conditions for Switching Positive T-S Fuzzy Interval Observes

In order to improve the conservatism of the standard conditions for the synthesis of positive switched interval state observers for system description with Metzler-Takagi-Sugeno fuzzy models, a new extended synthesis approach based on linear matrix inequalities is presented in he article. Taking into account a measurable set of premise variables, the associated structure with switching of positive fuzzy interval observers is designed to estimate the state of the system while maintaining quadratic stability and attenuating the influence on the dynamics of the observer from the additive disturbance bounded by the norm. The proposed structure of linear matrix inequalities reflects Metzler’s parametric constraints of positive systems, the fuzzy structure of the nonlinear switching system model, interval-defined system matrices and the principle of diagonal stabilization. The proposed method shows increased accuracy of the state estimation and ensures the observation of the state of the system in the interval of the lower and upper boundaries of the non-negative state of the system. The effectiveness of the presented theoretical conclusions is illustrated by a numerical example.