Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and H∞ Performance Conditions
ABSTRACT In this paper, new approaches to Hinfin controller design for a class of discrete-time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, two relaxed conditions of nonquadratic stability with H infin norm bound are presented for this class of systems. The two relaxed conditions are shown to be useful in designing fuzzy control systems. By introducing some additional instrumental matrix variables, the two relaxed conditions are used to develop Hinfin controllers. In the control design, the first relaxed condition has fewer inequality constraints, but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables. Finally, two examples are given to demonstrate the applicability of the proposed approach
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ABSTRACT: This paper deals with design procedures offuzzy controller and fuzzy observer, one of the mostimportant and basic concepts for fuzzy control systemdesign. Fuzzy controller guarantees stability of thewhole system i.e. fuzzy controller and fuzzy observer bythe Lyapunov stability approach, while fuzzy observerestimates states of the fuzzy dynamic plants. The twodesigns are formulated as two separate LMI feasibilityproblems using new non-quadratic stability conditionsbased on non-quadratic Lyapunov function andParallel distributed Compensation scheme to stabilizeTakagi-Sugeno (T-S) fuzzy systems. Then a separationproperty based on a vector comparison principle isapplied to check the stability of the whole system.Whereas, the obtained results are less conservative.Finally, numerical examples are presented to illustratethe effectiveness of our proposal by showing verysatisfactory results.Journal of Computer Science and Control Systems. 01/2010;
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ABSTRACT: This paper focuses on the problem of non-fragile guar-anteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS). Based on the parallel distributed compensation (PDC) approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations. The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities (BMIs). The Van de Vusse model is utilized to demon-strate the validity and effectiveness of the proposed approach. Keywords: discrete-time fuzzy bilinear system (DFBS), non-fragile control, guaranteed cost control, bilinear matrix inequality (BMI).Journal of Systems Engineering and Electronics 09/2010; 21:629-634. · 0.38 Impact Factor
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ABSTRACT: This paper focuses on the problem of Guaranteed cost control of uncertain T-S fuzzy systems. Based on observer design, the guaranteed cost output feedback control law which guarantees that the closed-loop uncertain T-S fuzzy system is robustly asymptotically stable is proposed. By utilizing the Lyapunov function together with the linear matrix inequality (LMI) approach and free weighting matrix method, some sufficient conditions are obtained, which guarantee the asymptotic stability of uncertain T-S fuzzy systems. A numerical example is included to show the proposed method is effective and can provide less conservative results.WSEAS Transactions on Systems 09/2011; 10(9):306-317.