New delay-dependent stability criteria for T–S fuzzy systems with time-varying delay

This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by a delay-partitioning approach. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then some tighter bounding inequalities, i.e., Peng-Park׳s integral inequality (reciprocally convex approach) and the Free-Matrix-Based integral inequality (which yields less conservative stability criteria than the use of Wirtinger-based inequality does) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of es and LMIs. Finally, a numerical example is included to show that the proposed methods are less conservative than existing ones.

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“…1 Table 2. It is seen from Table 2 that the results proposed in this paper are also significantly less conservative than that in [20,30,43,44].…”

Section: Numerical Examplementioning

confidence: 73%

Further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by delay-partitioning approach

et al. 2015

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“…These classes of systems are described as a weighted sum of some simple linear subsystems, and thus are easily analyzed. Since a T-S fuzzy model can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning (Takagi and Sugeno 1985), in recent years many studies have been done in the area of modeling systems with T-S models, see (Guan and Chen 2004;Lien 2006;Lien et al 2007;Liu 2008;Chen et al 2009;Zhang et al 2009;Hien 2010;Liu et al 2010;Da and He 2011) and the references cited therein. Time delays are unavoidable in various areas such as engineering systems, biology, and economics.…”

mentioning

confidence: 99%

“…The existence of time delays is often the main cause of instability and poor performance of a system. Therefore, the research on time-delay systems has attracted much attention in past years (Boyd et al 1994;Liu 2003aLiu , 2003bLiu , 2008Liu , 2010Guan and Chen 2004;Li, Wang, and Liao 2004;Lien et al 2007;Zhang et al 2009;Hien 2010;Liu et al 2010;Da and He 2011). Uncertainty in a control system may be attributed to modeling errors, measurement errors, parameter variations, and linearization approximations (Liu 2003b).…”

mentioning

confidence: 99%

“…Uncertainty in a control system may be attributed to modeling errors, measurement errors, parameter variations, and linearization approximations (Liu 2003b). Based on T-S fuzzy models, many researchers have investigated stability analysis and synthesis problems for time-delay systems (Guan and Chen 2004;Li, Wang, and Liao 2004;Lien 2006;Lien et al 2007;Hien 2010;Liu et al 2010; Da and He 2011). To weaken the conservatism of the conclusion, some assessments based on the Lyapunov second method have been carried out.…”

mentioning

confidence: 99%

“…To weaken the conservatism of the conclusion, some assessments based on the Lyapunov second method have been carried out. The delay-dependent stability of fuzzy systems with time delay was studied in Li, Wang, and Liao 2004;Lien 2006;Lien et al 2007;Liu 2008;Hien 2010;Liu et al 2010; Da and He 2011; and the exponential stable conditions of time-delay systems were presented in Zhang et al (2009), Hien (2010), and Da and He (2011). Recently, people have paid more and more attention to the robust stability of T-S fuzzy systems with time-varying delay.…”

mentioning

confidence: 99%

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Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

Liu

2015

Journal of the Chinese Institute of Engineers

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This paper concerns managing the robust exponential stability problem of uncertain Takagi-Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov-Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

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Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

Tan

Dian

Zhao

2017

Asian Journal of Control

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This paper discusses the issue of stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing an appropriate augmented fuzzy Lyapunov-Krasovskii functional (LKF) including non-quadratic Lyapunov matrices and triple and quadruple integral term,less conservative and newer stability conditions are introduced. In order to obtain stability conditions in the form of linear matrix inequalities (LMIs), some tighter bounding inequalities are employed to estimate the derivative of LKF. Several examples are provided to illustrate the effectiveness of the suggested approaches.

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New delay-dependent stability criteria for T–S fuzzy systems with time-varying delay

Cited by 111 publications

References 26 publications

Further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by delay-partitioning approach

Further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by delay-partitioning approach

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

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