In this study, the authors are concerned with a finite-dimensional guaranteed cost sampled-data fuzzy control problem, which is addressed for a class of non-linear Markov jump parabolic partial differential equation (...
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In this study, the authors are concerned with a finite-dimensional guaranteed cost sampled-data fuzzy control problem, which is addressed for a class of non-linear Markov jump parabolic partial differential equation (MJPPDE) systems. Applying the Galerkin's method to the MJPPDE system, a non-linear Markov jump ordinary differential equation (MJODE) system is derived. The resulting non-linear MJODE system can describe the dominant dynamics of the MJPPDE system, which is subsequently expressed by the Takagi-Sugeno (T-S) fuzzy model. Then, a guaranteed cost sampled-data fuzzy controller is developed to stabilise the closed-loop slow fuzzy system exponentially in the mean-square sense while providing an upper bound for the quadratic cost function. Making full use of their special features, they will be able to establish the bound on t. The authors' theory enables us to guarantee the existence of the feedback controller and to judge the effectiveness of the feedback control based on the sampled-data to stabilise the given system in the sense of mean-square exponential stability.
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