Stability criteria for uncertain Takagi–Sugeno fuzzy systems with interval time-varying delay

Lien, Chang‐Hua; Yu, Ker‐Wei; Chen, W.D.; Zhang, Wan; Chung, Yeong-Jay

doi:10.1049/iet-cta:20060299

Cited by 103 publications

(95 citation statements)

References 13 publications

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“…It can be concluded that the obtained results in this paper are less conservative than those of [4,7], [34][35][36]. Moreover, if we assume timevarying delay .t/ satisfies (2), the delay-dependent fault estimation conditions proposed in [21][22][23][24][25], [27] fail to give a feasible solution.…”

Section: Numerical Examplementioning

confidence: 76%

“…Moreover, the interval OE 1 ; 2 is divided into two unequal variable subintervals OE 1 ; 1 C ı and OE 1 C ı; 2 .0 < < 1; ı D 2 1 / in which is a tunable parameter. It is clear that both the information of delayed state e n .t n N 1 /.n D 1; 2; 3; :::N / and e n .t 1 ı/.0 < < 1/ can be taken into account, the Lyapunov-Krasovskii functional defined in Theorem 3.1 is more general than the one in [4][5][6][7], [34][35][36][37]. Therefore, the result of fault estimation of Theorem 3.1 and the stability criterion of Corollary 3.2 can further reduce the analysis and synthesis conservatism.…”

Section: Actuator Fault Estimationmentioning

confidence: 99%

“…Considering interval time-varying delay, the upper delay bounds 2 derived from [4][5][6][7], [37] and the method proposed in this paper are tabulated in Table 1 Example 4.2. Consider a two rule T-S fuzzy system borrowed from [4,7], [34][35][36]:…”

Section: Numerical Examplementioning

confidence: 99%

See 2 more Smart Citations

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Sun

Wang

2016

Open Mathematics

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This paper addresses the problem of robust fault-tolerant control design scheme for a class of TakagiSugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H 1 constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered interval time delay is designed to compensate for the impact of actuator faults, while guaranteing that the closed-loop system is asymptotically stable with the prescribed H 1 performance. Moreover, all the obtained less conservative sufficient conditions for the existence of fault estimation observer and fault-tolerant controller are formulated in terms of linear matrix inequalities. Finally, the numerical examples and simulation results are presented to show the effectiveness and merits of the proposed methods.

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Section: Numerical Examplementioning

confidence: 76%

Section: Actuator Fault Estimationmentioning

confidence: 99%

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Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Sun

Wang

2016

Open Mathematics

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“…Our study in this paper makes some initial attempt to stability analysis for interval delayed T-S fuzzy systems. Although our modeling is for the T-S fuzzy systems with interval time-varying delays [12,21,22,27], it is also applicable to the uncertain systems in terms of [1,18] and the networked control systems [3,15,19], while the proposed results can be extended to H ∞ control [3,15,22,27].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach

An¹,

Liu²,

Wen³

2017

J. Nonlinear Sci. Appl.

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This paper is concerned with the problem of the stability analysis for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. The delay is assumed to be differential with interval bounds, and has both the lower and upper bounds of the delay derivatives, in which the upper bound of delay derivative may be greater than one. By constructing some delaydependent Lyapunov functions, some stability criteria are derived by using the convex optimization method and new integral inequality techniques. Utilizing integral inequalities for quadratic functions plays a key role in the field of stability analysis for delayed T-S fuzzy systems, and some integral inequalities for quadratic functions are derived and employed in order to produce tighter bounds than what the Jensen inequality and Wirtinger-based inequality produce. Then, less conservative stability criteria are derived by using convex combination method and improved integral inequalities based on appropriate Lyapunov-Krasovskii (LK) functional. Finally, several examples are given to show the advantages of the proposed results.

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“…Such uncertainties may be due to measurement error, simplified models of natural laws, neglected dynamics, or inevitably uncertain model. In recent years, a variety of methodologies in robust control have been studied and proposed, such as adaptive control approach, differential inequality approach, sliding mode control approach, ∞ control approach, adaptive sliding mode control approach, time-domain approach, backstepping control approach, neural-fuzzy approach, LMI approach, and others; see, for instance [1][2][3][4][5][6][7][8][9][10][11][12] and the references therein. In [8], based on the time-domain approach with differential inequality, a feedback control has been proposed to accomplish generalized exponential synchronization for a pair of mechanical systems with uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization for a Class of Uncertain Nonlinear Systems via a Novel Hybrid Control Applicable to Mechanical Systems

Sun

2014

Advances in Mechanical Engineering

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An important consideration in control system design is that of model uncertainty. Besides, systems with mixed uncertainties, chaotic vibrations, and input nonlinearities are not easily stabilized and traditional control schemes for linear systems are not always effective. Therefore, in this paper, we will solve two problems, first searching a novel hybrid control methodology to achieve the practical stabilization for uncertain systems with mixed uncertainties and second calculating the guaranteed exponential convergence rate with the convergence radius. The applicability of the main results is demonstrated by a tracking controller design for a class of uncertain nonlinear mass-damper-spring systems with mixed uncertainties, chaotic vibrations, and input nonlinearities.

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Stability criteria for uncertain Takagi–Sugeno fuzzy systems with interval time-varying delay

Cited by 103 publications

References 13 publications

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach

Robust Stabilization for a Class of Uncertain Nonlinear Systems via a Novel Hybrid Control Applicable to Mechanical Systems

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