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This paper is concerned with the problem of model reduction for discrete-time Takagi–Sugeno (T–S) fuzzy state-delay systems with finite-frequency input signals. A new finite-frequency model reduction algorithm is proposed, which can get a better approximation performance than the existing full-frequency methods. Firstly, a finite-frequency H ∞ performance index is defined in the frequency domain. Then, a stability condition and a finite-frequency H ∞ performance analysis condition are developed by the aid of Jensen׳s inequality and Parseval׳s theorem, respectively. Based on these conditions, sufficient model reduction conditions are derived for discrete-time T–S fuzzy state-delay systems. An optimization algorithm is proposed to obtain a stable reduced-order model satisfying the finite-frequency performance specification. Finally, the effectiveness of the proposed method is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the problem of observer-based output feedback control design of discrete-time Takagi–Sugeno (T–S) fuzzy systems is investigated based on a multi-samples method. In order to ameliorate the existing results in the literature, a fuzzy observer-based output feedback controller, which relies on multi-samples normalized fuzzy weighting functions, is developed for relaxing the design conditions of observer-based output feedback control. Moreover, thanks to the special form of the developed observer-based output feedback controller, it is shown that all the designed parameters can be solved via a set of strict linear matrix inequalities, i.e., the drawback induced by the usual two-step method is resolved by means of a compromising way. Finally, the benefit of the proposed result is validated by using some numerical experiments. [ABSTRACT FROM AUTHOR]