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【期刊论文】A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays
IEEE Transactions on Fuzzy Systems,2012,21(4):655 - 671
2012年11月12日
This paper focuses on analyzing a new model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new comparison model is proposed by employing a new approximation for time-varying delay state, and then, a delay partitioning method is used to analyze the scaled small gain of this comparison model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced ℓ 2 disturbance attenuation performance, is derived by employing the scaled small-gain theorem. Then, the solvability condition for the induced ℓ 2 DOF control is also established, by which the DOF controller can be solved as linear matrix inequality optimization problems. Finally, examples are provided to illustrate the effectiveness of the proposed approaches.
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IEEE Transactions on Fuzzy Systems,2013,22(1): 124 - 138
2013年03月07日
This paper is concerned with the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation and time-varying state delay. By means of the delay-partitioning method and slack variables, a novel fuzzy Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Then, the delay-dependent stabilization approach, which is based on a nonparallel distributed compensation scheme, is introduced for the closed-loop fuzzy systems. Finally, illustrative examples are provided to illustrate the feasibility and effectiveness of the proposed methods.
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IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics),-0001,41(1): 273 - 286
-1年11月30日
This paper investigates the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. Based on a novel fuzzy Lyapunov-Krasovskii functional, a delay partitioning method has been developed for the delay-dependent stability analysis of fuzzy time-varying state delay systems. As a result of the novel idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. A delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is given for the closed-loop fuzzy systems. The proposed stability and stabilization conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved readily by using existing LMI optimization techniques. Finally, two illustrative examples are provided to demonstrate the effectiveness of the techniques proposed in this paper.
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【期刊论文】L2– L∞ Control of Nonlinear Fuzzy ItÔ Stochastic Delay Systems via Dynamic Output Feedback
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics),2009,39(5):1308 - 131
2009年03月24日
This paper addresses the L 2 - L infin dynamic output feedback (DOF) control problem for a class of nonlinear fuzzy Ito stochastic systems with time-varying delay. The focus is placed upon the design of a fuzzy DOF controller guaranteeing a prescribed noise attenuation level in an L 2 - L infin sense. By using the slack matrix approach, a delay-dependent sufficient condition is derived to assure the mean-square asymptotic stability with an L 2 - L infin performance for the closed-loop system. The corresponding solvability condition for a desired L 2 - L infin DOF controller is established. Since these obtained conditions are not all expressed in terms of linear matrix inequality (LMI), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be easily solved numerically. Finally, numerical results are presented to demonstrate the usefulness of the proposed theory.
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【期刊论文】H∞ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics),2012,42(6):1574 - 158
2012年05月18日
This paper is concerned with the problem of H ∞ model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H ∞ performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
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