Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems With Mismatched Premise Membership Functions

Lam, Hak‐Keung; Tsai, Shun-Hung

doi:10.1109/tfuzz.2013.2243735

Cited by 109 publications

(67 citation statements)

References 31 publications

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“…To facilitate the stability analysis, polynomial functions approximating w i (x)m j (y) [33], [50] are first constructed. However, it may require a high degree of polynomial for good approximation, which will demand high computational power for solving a feasible solution.…”

Section: B Stability Analysis Of Static Output Feedback Ppfmb Contromentioning

confidence: 99%

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper deals with the static output feedback stabilization of positive polynomial fuzzy-model-based (PPFMB) control systems. The positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to non-convex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions which carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares (SOS) are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.

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Section: B Stability Analysis Of Static Output Feedback Ppfmb Contromentioning

confidence: 99%

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…Instead, numerical results could be found based on SOS approach with, for example, the third-party toolbox SOSTOOLS [31]. Some of the recent research on polynomial fuzzymodel-based systems are listed as follows, for example, [32] studied stability analysis via approximated membership functions considering sector nonlinearity of control input, [33] studied stability analysis with mismatched premise membership functions and [34] studied stability analysis using switching polynomial Lyapunov function. Most of the existing works on polynomial fuzzy systems are with type-1 membership functions and very few works have been reported to study the interval type-2 polynomial fuzzy-model-based systems, which is the key motivation of this paper.…”

Section: Introductionmentioning

confidence: 99%

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

Li¹,

Lam²,

Zhang

2017

IET Control Theory & Applications

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Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract: In this paper, the problems of stabilization for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, we formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

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“…In the literature such as the work mentioned above, most of the stability analysis are MFI that the information of membership functions is not taken into account and thus it potentially leads to conservative analysis results. To relax the conservativeness of stability analysis results through the use of membership function information, different types of membership functions such as piecewise-linear membership functions [18], polynomial membership functions [17] and mismatched premise membership functions [23] have been proposed for the MFD stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Membership‐Function‐Dependent Stability Analysis of Interval Type‐2 Polynomial Fuzzy‐Model‐Base Control Systems

Song

Lam

Yang

2017

IET Control Theory & Applications

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Abstract:In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. In order to tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. To improve the design flexibility and reduce the implementation costs, the IT2 polynomial fuzzy controller does not need to share the same premise membership functions nor the same number of rules with the IT2 polynomial fuzzy model. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions membership function dependent, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical Examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.

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Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems With Mismatched Premise Membership Functions

Cited by 109 publications

References 31 publications

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

Membership‐Function‐Dependent Stability Analysis of Interval Type‐2 Polynomial Fuzzy‐Model‐Base Control Systems

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