Choice of conjunctive operator of TSK fuzzy systems and stability domain study

Benrejeb, Mohamed; Sakly, Anis; Othman, Kamel Ben; Borne, Pierre

doi:10.1016/j.matcom.2007.04.003

Cited by 27 publications

(24 citation statements)

References 6 publications

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“…In this section, stability conditions for the Lur'e Postnikov systems (6) - (7) are developed using the Borne and Gentina stability criterion [10][11][12] (Appendix) and the Benrejeb arrow form matrix [4][5][6][7]. Moreover, a stabilizing dead-beat controller for the nonlinear studied system (4) or (6) - (7) exploiting the controller parameters of the linearized system (13) with (14) - (16) or (17) is proposed.…”

Section: Stability Convergence Conditions For Nonlinear Systemsmentioning

confidence: 99%

“…Let (S) be a Lur'e-type system of the form (4) or (6)- (7), a j , ∀ j=1 ,2 ,…,n−1 ,a i ≠a j , ∀i≠j be distinct arbitrary constant parameters and β j , γ j and γ n be parameters expressed respectively by [4][5][6][7].…”

Section: Lur'e System Stability Analysismentioning

confidence: 99%

“…By applying the Borne and Gentina practical stability criterion [11,12] to the discrete Lur'e type system (4) or (6) - (7) characterized by the Benrejeb arrow form matrix [4][5][6][7], it comes the following theorem [30].…”

Section: Lur'e System Stability Analysismentioning

confidence: 99%

“…Let consider the Lur'e type system (S) of the state representation form (6). A change of coordinate defined by y k =Tx k with y k ∈ℜ n and T ∈ℜ n×n inversible, defined by…”

Section: Lur'e System Stability Analysismentioning

confidence: 99%

See 3 more Smart Citations

Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

Sfaihi¹,

Fekih²,

Benrejeb³

2016

SIC

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Abstract:In this paper, a constructive design methodology for Finite-Time Stability (FTS) of a class of nonlinear discrete-time systems is proposed. A dead-beat controller that can achieve n-finite-time stability is constructed. Furthermore, stability conditions, based on the use of Borne and Gentina practical stability criterion and matrices in the Benrejeb arrow form, are synthesized. Similarity between transient behaviors of dead-beat controlled linearized and nonlinear third order systems are shown and concluding remarks are formulated.

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Section: Stability Convergence Conditions For Nonlinear Systemsmentioning

confidence: 99%

Section: Lur'e System Stability Analysismentioning

confidence: 99%

Section: Lur'e System Stability Analysismentioning

confidence: 99%

“…Let consider the Lur'e type system (S) of the state representation form (6). A change of coordinate defined by y k =Tx k with y k ∈ℜ n and T ∈ℜ n×n inversible, defined by…”

Section: Lur'e System Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

Sfaihi¹,

Fekih²,

Benrejeb³

2016

SIC

Self Cite

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“…To overcome limitations due to the existence of Lyapunov-Krasovskii functionals, we propose, in this paper, to study the stability of TS fuzzy switched systems through the convergence of a regular vector norm, associated with a specific characteristic matrix, called arrow form matrix [36][37][38][39][40][41][42][43]. The proposed method is based on the construction of a common overvaluing/comparison system for all the fuzzy submodels and whose stability permits concluding to that of the original system.…”

Section: Introductionmentioning

confidence: 99%

Delay‐Dependent Stability Analysis of TS Fuzzy Switched Time‐Delay Systems

Aoun

Kermani

Sakly

2017

Mathematical Problems in Engineering

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This paper proposes a new approach to deal with the problem of stability under arbitrary switching of continuous-time switched time-delay systems represented by TS fuzzy models. The considered class of systems, initially described by delayed differential equations, is first put under a specific state space representation, called arrow form matrix. Then, by constructing a pseudoovervaluing system, common to all fuzzy submodels and relative to a regular vector norm, we can obtain sufficient asymptotic stability conditions through the application of Borne and Gentina practical stability criterion. The stability criterion, hence obtained, is algebraic, is easy to use, and permits avoiding the problem of existence of a common Lyapunov-Krasovskii functional, considered as a difficult task even for some low-order linear switched systems. Finally, three numerical examples are given to show the effectiveness of the proposed method.

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Fuzzy Random Variable

Wang

Watada

2012

Fuzzy Stochastic Optimization

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Choice of conjunctive operator of TSK fuzzy systems and stability domain study

Cited by 27 publications

References 6 publications

Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

Delay‐Dependent Stability Analysis of TS Fuzzy Switched Time‐Delay Systems

Fuzzy Random Variable

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