Abstract
The problem of an unmatching observer-based controller design for discrete-time fuzzy systems with time delay is investigated, in which the fuzzy controller shares different membership functions from the fuzzy model. The objective is to design a state observer and unmatching fuzzy controller such that the discrete closed-loop system with time delay is asymptotically stable. A sufficient condition that contains the information of the membership functions of fuzzy model and fuzzy controller for the stabilization via an unmatching observer-based output feedback is presented. The proposed control scheme is well capable of enhancing the design flexibility, and the stability condition is less conservative. Three numerical examples are given to illustrate the effectiveness and advantages of the proposed method.
Highlights
Time-delay phenomena intensively exist in natural science and engineering and social life, such as nonlinear and timedelay models
A single-step linear matrix inequality method is developed for the observer-based controller design for discrete-time fuzzy systems in [9], which overcomes the drawbacks induced by the conventional two-step approach, and yields less conservative results. e problem of fuzzy observer-based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties in [10]
We focused on the observer-based stabilization control for discrete-time T-S fuzzy time-delay systems and a novel observer-based output feedback controller is investigated for the discrete-time T-S fuzzy timedelay systems. e main contributions of this paper can be summarized as follows: (i) As the membership functions of the fuzzy model and the fuzzy controller are all considered in the analysis, some membership-function-dependent stability conditions are derived, which are less conservative than membership-function-independent stability conditions (ii) As the membership functions of the controller are distinctive from those of the fuzzy model, the membership functions can be chosen arbitrarily, which makes a higher degree of design flexibility of the fuzzy controller achieved, and its structure can be further simplified e remainder of this paper is organized as follows
Summary
Time-delay phenomena intensively exist in natural science and engineering and social life, such as nonlinear and timedelay models. Erefore, state estimation and observation of nonlinear systems are important but challenging problems in modern control theory. A single-step linear matrix inequality method is developed for the observer-based controller design for discrete-time fuzzy systems in [9], which overcomes the drawbacks induced by the conventional two-step approach, and yields less conservative results. E problem of fuzzy observer-based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties in [10]. Some results related to the observer-based controller design problem have been extended to the MIMO time-delay systems in [14]. Erefore, the observer-based stabilization control for the discrete-time T-S fuzzy systems with time delay is an important topic. We use wi, mi instead of wi(z(t)), mi(z(t))
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