Robust H∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions

Zhou, Shaosheng; Feng, Gang; Lam, James; Xu, Shengyuan

doi:10.1016/j.ins.2004.07.015

Cited by 168 publications

(109 citation statements)

References 25 publications

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“…Obviously, the main drawback of the approach developed in this paper is the conservatism introduced at the moment of searching for the common matrix P. However, this disadvantage can be reduced by applying the methods presented in [18][19][20][21], where piecewise or fuzzy Lyapunov functions are considered in order to relax the stability analysis of the TS fuzzy systems.…”

Section: Remark 15mentioning

confidence: 99%

The optimal fuzzy robust regulator for TS discrete‐time systems: An LMI approach

Meda-Campaña

Castillo–Toledo

2008

Adaptive Control & Signal

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In this work, the problem of designing an optimal regulator for discrete-time nonlinear systems when the plant can be modelled by a Takagi-Sugeno (TS) fuzzy system is addressed. The approach analyzed in this paper, under certain conditions, guarantees the tracking of references and allows the performance of the controller to be improved by means of the inclusion of some cost functions. The main result is given in terms of linear matrix inequality techniques, meaning that the design of the controller can be obtained in a practical way. Finally, numerical simulations are carried out in order to illustrate the validity of the fuzzy regulator.

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Section: Remark 15mentioning

confidence: 99%

The optimal fuzzy robust regulator for TS discrete‐time systems: An LMI approach

Meda-Campaña

Castillo–Toledo

2008

Adaptive Control & Signal

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“…Based on these stability and robust stability analysis, numerous systematic design schemes have been proposed to synthesize the T-S fuzzy controllers in order to guarantee the stability or performances of the overall T-S fuzzy control systems even in the presence of parameter uncertainties 6,7,8 . Most of the above work is discussed only in the time domain, and the results are mainly presented in the form of Linear Matrix Inequalities (LMIs).…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Type of T-S Fuzzy Control Systems Using Off-Axis Circle Criterion

Cao¹,

Xiao²,

Huang³

et al. 2012

IJCIS

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“…To overcome the conservatism arising from the use of a single Lyapunov matrix, more effective Lyapunov methods have been presented such as piecewise quadratic Lyapunov functions [15,16], the weighting-dependent Lyapunov functions [17,18] and Polya's theorem [19]. It is noted that all of the aforementioned research efforts have been focused on PDC law.…”

Section: Introductionmentioning

confidence: 99%

Stabilization for discrete-time fuzzy systems with Takagi-Sugeno’s models: reduce the complexity

Wang

Liu

2010

Sci. China Inf. Sci.

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The problem of sate feedback control for discrete-time fuzzy systems with Takagi-Sugeno's models is investigated to reduce the computational burden. A stabilization condition is obtained by applying a new Lyapunov function. It is shown that our new theorem is equivalent to an existing result in guaranteeing the stability of the fuzzy system but consumes less computational time than the latter. The effectiveness and the superiority of the proposed design approach are demonstrated by an example borrowed from the literature.Keywords Takagi-Sugeno's fuzzy model, non-quadratic Lyapunov function, linear matrix inequality CitationWang L K, Liu X D. Stabilization for discrete-time fuzzy system with Takagi-Sugeno's models: reduce the complexity.

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Robust H∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions

Cited by 168 publications

References 25 publications

The optimal fuzzy robust regulator for TS discrete‐time systems: An LMI approach

The optimal fuzzy robust regulator for TS discrete‐time systems: An LMI approach

Stability Analysis of a Type of T-S Fuzzy Control Systems Using Off-Axis Circle Criterion

Stabilization for discrete-time fuzzy systems with Takagi-Sugeno’s models: reduce the complexity

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