This paper presents the piecewise Lyapunov functions based the delay- independent Hinfin controller design for a class of time-delay T-S fuzzy system. First, we apply a piecewise observer to estimate the states. Then, a piecewise delay-independent Hinfin controller is designed to guarantee the Hinfin performance. Subsequently, the problem of control design is characterized in terms of two LMIs, one for the control gain and the other for observer gain, and the LMIs can be effectively solved by convex optimization technique. Simulation results demonstrate the applicability and the effectiveness of the proposed controller.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise 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. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H infinity controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.
[Show abstract][Hide abstract] ABSTRACT: "For original paper see Y. S. Yang, C. J. Zhou, ibid., vol. 13, no. 1, p. 104-114, (2005)". In this note, we point out some mistakes in a 2005 paper by Yang and Zhou.
IEEE Transactions on Fuzzy Systems 07/2009; 17(3-17):732 - 733. DOI:10.1109/TFUZZ.2008.924199 · 8.75 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this note, the problem of decentralized model reference adaptive variable structure control for a class of perturbed large-scale systems with varying time-delay interconnections is investigated. Based on the Lyapunov stability theorem, an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed. The use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved. Once the system enters the sliding manifold, the dynamics of controlled systems are insensitive to matching perturbations. Finally, an example is given to demonstrate the feasibility of the proposed control scheme.
IEEE Transactions on Automatic Control 08/2003; 48(7-48):1213 - 1217. DOI:10.1109/TAC.2003.814263 · 2.78 Impact Factor
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