A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems

IEEE Transactions on Fuzzy Systems (Impact Factor: 8.75). 08/2011; 19(4):785-791. DOI: 10.1109/TFUZZ.2011.2142315
Source: DBLP


This paper presents a new fuzzy Lyapunov function (FLF) for the stability analysis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. Unlike conventional FLFs, the proposed one depends not only on the fuzzy weighting functions of the T-S fuzzy systems but on their first-order time derivatives as well. Based on the proposed FLF, a sufficient stability condition is derived in the form of linear matrix inequalities, depending on the upper bounds on the second-order time derivative of the fuzzy weighting functions, as well as the first-order ones. Finally, some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature.

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Available from: Young Hoon Joo, Jan 25, 2014
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    • "matrix is used for all local models of fuzzy systems, the quadratic Lyapunov function approach often leads to conservative results. Then, parameter-dependent Lyapunov functions (or called fuzzy Lyapunov functions) [11], [17], [19], [24], [36], piecewise Lyapunov functions [13], [23], and k-sample variation Lyapunov functions [16] are, respectively, proposed for reducing the conservatism introduced by using quadratic Lyapunov functions. On the other hand, by sharing the same fuzzy rules with the fuzzy models, parallel distributed compensation (PDC) control schemes [29] are often used for designing fuzzy controllers in the existing literature. "
    Dataset: Dong J2015a

    Full-text · Dataset · Jan 2016
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    • "In general, a common quadratic Lyapunov function approach was used to deal with stability and stabilization issues for type-1 T–S fuzzy systems. Several nonquadratic Lyapunov functions were also proposed to derive less conservative results [6] [7] [8] [9] [10] [11] [12] [13] [14]. On the other hand, most existing results were obtained by parallel distributed compensation (PDC) scheme. "
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    ABSTRACT: Interval type-2 (IT2) T–S fuzzy model is a useful tool to represent nonlinear systems subject to parameter uncertainties. This study focuses on designing controllers of IT2 T–S fuzzy systems via dynamic output feedback strategy. The IT2 fuzzy closed-loop systems are represented as descriptor system form for obtaining stability conditions in terms of linear matrix inequalities (LMIs). Membership-function-independent stability conditions for the IT2 fuzzy closed-loop systems are derived by Lyapunov-based approach. The information of the lower and upper membership functions is employed to introduce several slack matrices in the stability analysis and to further relax the obtained results. Numerical examples are provided to illustrate the effectiveness of the proposed method.
    Full-text · Article · Mar 2015 · Neurocomputing
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    • "However, it is usually difficult to find efficient numerical algorithms to solve such coupled HJEs or HJIs. For several decades, the Takagi–Sugeno (T–S) fuzzy model has been widely applied for the control design of nonlinear systems [5] [10] [21] [27] [37], since it can approximate any smooth nonlinear system to any specified accuracy by blending a family of local linear models through fuzzy membership functions. Recently, the T–S fuzzy model has been employed to deal with the control and filter problems of nonlinear stochastic systems with multiplicative noise [1] [25] [26]. "
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    ABSTRACT: In this paper, the observer-based H∞ control problem is investigated for a class of T-S fuzzy nonlinear stochastic systems with multiplicative noise and successive packet dropouts. The stochastic system under study is subject to state- and disturbance-dependent noises, and the successive packet dropouts are assumed to obey the Bernoulli random binary distribution. By employing the stochastic analysis approach, a sufficient condition is derived such that the closed-loop system is stochastically stable, and the prescribed H∞ disturbance-rejection-attenuation performance is also achieved. Moreover, the observer-based H∞ fuzzy controller design method is proposed in terms of linear matrix inequalities for the systems with successive packet dropouts. Finally, a numerical example is exploited to demonstrate the effectiveness of the obtained results.
    Full-text · Article · Jan 2015
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