Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and H∞ Performance Conditions

Dept. of Autom., Hangzhou Dianzi Univ., Zhejiang
IEEE Transactions on Fuzzy Systems (Impact Factor: 8.75). 04/2007; 15(2):188-199. DOI: 10.1109/TFUZZ.2006.879996
Source: IEEE Xplore


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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    • "Using the quadratic (non-quadratic) Lyapunov function, some scholars have derived the relaxed stability conditions for T–S fuzzy systems (see222324252627282930313233and references therein), but the Brownian motions were not considered for the systems192021222324252627282930313233. Compared with the approaches of192021222324252627282930313233, PDC and non-PDC fuzzy control design methods with relaxed stability conditions for continuous-time multiplicative noised fuzzy systems were proposed in[34]. However, to the best of our knowledge, the mean-square admissibility problem of stochastic T–S fuzzy singular systems has not yet been fully investigated. "
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    ABSTRACT: The mean-square admissibility problem of stochastic T–S fuzzy singular systems via an extended quadratic Lyapunov function is investigated in this paper. Comparing with the existing quadratic Lyapunov function method, the extended quadratic Lyapunov function method can relax stabilization conditions. Firstly, the sufficient condition is given for the mean-square admissibility of stochastic T–S fuzzy singular systems based on an extended quadratic Lyapunov function approach. Secondly, two sufficient conditions for mean-square admissibility of closed-loop systems via the parallel distributed compensation (PDC) fuzzy controller and non-parallel distributed compensation (non-PDC) fuzzy controller are proposed. Furthermore, through the extended quadratic Lyapunov function method and non-PDC fuzzy controller, the less conservative mean-square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities (LMIs). Finally, some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology.
    No preview · Article · Jan 2016 · Fuzzy Sets and Systems
    • "The most popular type of fuzzy controller is the state-feedback fuzzy controller (referred to as fuzzy controller hereafter), which is employed to close the feedback loop for the control process. Other fuzzy controllers, such as the adaptive fuzzy controller [7]–[18], decentralized fuzzy controller [19], fuzzy sliding-mode controller [20]–[27], fuzzy controller with fault-tolerant design [28], fuzzy controller for time-delay systems [29], H ∞ fuzzy controller [30], [31], output-feedback fuzzy controller [32], switching fuzzy controller [33]–[39], sampled-data fuzzy controller [40]–[45], and 2-D fuzzy controller [46], can also be found in the literature. "
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    ABSTRACT: This paper investigates the stability of a polynomial-fuzzy-model-based (PFMB) control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. Three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched/mismatched number of rules and/or premise membership functions, which demonstrate different levels of controller complexity, design flexibility, and stability analysis results. A general polynomial Lyapunov function candidate is proposed to investigate the system stability. Unlike the published work, there is no constraint on the polynomial Lyapunov function candidate, which is independent of the form of the polynomial fuzzy model. Thus, it can be applied to a wider class of PFMB control systems and potentially produces more relaxed stability analysis results. Two-step stability conditions in terms of sum-of-squares (SOS) are obtained to numerically find a feasible solution. To facilitate the stability analysis and relax the stability analysis result, the boundary information of membership functions is taken into account in the stability analysis and incorporated into the SOS-based stability conditions. Simulation examples are given to illustrate the effectiveness of the proposed approach.
    No preview · Article · Jun 2015 · IEEE Transactions on Fuzzy Systems
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    • "Takagi-Sugeno(T-S) model fuzzy systems have been extensively studied in the past decades since T-S fuzzy models can be used to effectively represent a large class of nonlinear systems. Many controller design problems for T-S model fuzzy systems have been considered in the literature [16]– [19]. The most frequently used control design method is the so-called parallel distribution compensation (PDC), by which the controller shares the same fuzzy premise variables and membership functions with the T-S fuzzy plant. "
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    ABSTRACT: This paper considers the H∞ control problem for discrete-time Takagi-Sugeno (T-S) model fuzzy systems with event-triggered output feedback. The measurement output is transmitted to a fuzzy controller when the output error exceeds a pre-given threshold. The parallel distribution compensation (PDC) can not be used for controller design since the controller may not receive enough information about premise variables of the plant due to the event-triggered transmission scheme. A fuzzy dynamical output feedback controller is proposed to regularly generate the control input, which makes the controlled system stable with a certain H∞ disturbance attenuation level. A numerical example is given to show the effectiveness of the proposed approach.
    Full-text · Conference Paper · Jan 2013
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