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 $τ$ . 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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Errata

An Erratum has been published for this content:

Corrigendum: Finite-dimensional guaranteed cost sampled-data fuzzy control of Markov jump distributed parameter systems via T–S fuzzy model

Finite-dimensional guaranteed cost sampled-data fuzzy control of Markov jump distributed parameter systems via T–S fuzzy model

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