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The problem of enhanced stabilization of discrete-time Takagi–Sugeno fuzzy system is investigated in depth via proposing a new way to employ much more information implied in various time-varying differences of multi-instant normalized fuzzy weighting functions. Benefit from the given comprehensive real-time scheduling model, these time-varying differences on time vertical dimension and two different transverse dimensions are for the first time integrated into fuzzy stabilization and two key alterable weights are also introduced. Consequently, much considerable freedom can be produced and, thus, it brings much less conservative results than the reported ones in recent literature. More importantly, a very simple workable way has been provided to online recognize the specific enabled mode at each sampling instant so that those existing time-consuming online operations in referred literature can be avoided to ease online implementation costs. Indeed, this feature is very beneficial to the practical application of our theoretical results. Finally, the superiority of our developed method over previous ones is validated adequately via two benchmark simulations. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reducing the conservatism for stabilization of discrete-time Takagi–Sugeno fuzzy systems via a new extended representation approach. Different from previous slack variable methods, an advanced slack variable method without limitations is proposed for further making good use of available fuzzy weighting functions. Owing to the introduction of extended representations for homogenous polynomials, those strong limitations in recent literature are relaxed and thus the primary and secondary sequences of all normalized fuzzy weighting functions can be mapped to one augmented multi-indexed matrix for each homogeneous polynomial. Therefore, less conservative stabilization conditions can be provided as a result of these effective measures and thus a part of the online computational cost is transferred to the offline implementation. Finally, the benefits of the proposed method are illustrated by means of numerical experiments. [ABSTRACT FROM AUTHOR]

This paper is focused on the issue of scheduling stabilization of Takagi–Sugeno fuzzy control systems by the aid of digging down much deeper of implicit information in the underlying systems. An event-triggered real-time scheduler that decides which control mode should be executed at any given instant is constructed by periodically evaluating the joint-distribution-type of multi-instant normalized fuzzy weighting functions at every sampled instant. Profiting from the proposed event-triggered scheduling policy, the proper control mode for the current instant is updated in order to adapt time-varying situations once if the underlying joint-distribution-type changes, and thus previous implementations of control tasks with an unchanged control mode can be further relaxed in this paper. The effectiveness of our approach is verified by several simulation examples in the end. [ABSTRACT FROM AUTHOR]