Piecewise H infinity: controller design of discrete time fuzzy systems.
ABSTRACT This paper presents a new H infinity controller design method for the discrete time fuzzy systems based on the piecewise Lyapunov functions. The basic idea of the proposed approach is to construct the controller for the fuzzy systems in such a way that a discrete time piecewise Lyapunov function can be used to establish the global stability with H infinity-disturbance attenuation performance of the resulting close loop fuzzy control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically tractable with commercially available software. Numerical example is given to demonstrate the advantage of the proposed method.
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ABSTRACT: Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussedIEEE Transactions on Fuzzy Systems 11/2006; DOI:10.1109/TFUZZ.2006.883415 · 6.31 Impact Factor
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ABSTRACT: En este trabajo se revisa el estado del arte sobre estabilidad de sistemas borrosos, poniéndose de manifiesto las dificultades para su análisis, debido a la característica falta de linealidad de los mismos. Se revisan los estudios basados en el criterio del círculo, las técnicas para calcular índices de estabilidad, así como técnicas basadas en aplicación del teorema de estabilidad de Lyapunov, que permite utilizar métodos numéricos de búsqueda de soluciones. Además, se revisan los trabajos de estabilidad mediante el uso del modelo borroso de Takagi-Sugeno (T-S), el enfoque de las Desigualdades Matriciales Lineales (LMI), que ha tenido un interés creciente en los últimos años, así como otra línea de investigación basada en estabilidad energéticaRevista iberoamericana de automática e informática industrial (RIAI) 04/2007; 4(2). DOI:10.1016/S1697-7912(07)70205-4 · 0.05 Impact Factor
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ABSTRACT: This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 11/2008; 38(5):1390-401. DOI:10.1109/TSMCB.2008.927267 · 3.78 Impact Factor