Improved stability criterion for linear systems with two additive time-varying delay

Tang, Hongji; Han, Yang; Xiao, Xiaoqing; Yu, Hongwang

doi:10.1109/chicc.2016.7553325

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…In [30], [31], to improve conservatism of the stability condition, the relationship between the timevarying delay and its upper bound was further considered in the process of estimating the derivative of LKF. Besides, many researchers have tried to achieve a MUBTD guaranteeing asymptotic stability [26], [32], [33], [34], [35]. More recently, the authors of [36] tried to take into account more information of system with ATDs by introducing an improved delay interconnection integral terms.…”

Section: Introductionmentioning

confidence: 99%

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

2020

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This paper is concerned with the problem of stability analysis for systems with additive time-varying delays (ATDs). This paper proposes a new free-matrix-based integral inequality that provides estimate of the energy of the vector that contains the state and its derivative at the same time. Consequently, the proposed inequality enables the Lyapunov-Krasovskii functional (LKF) to take into account not only the respective energies of the state and its derivatives but also the correlated effect of them. Then, based on the proposed inequality, this paper derives a new stability criterion of systems with ATDs. This paper constructs LKF by proposing new sets of multiple subintervals of the ATDs, and makes use of the proposed inequality when estimating the derivatives of the LKF. This allows the resulting stability criterion to take full advantage of the information of the multiple subintervals of the ATDs. This paper also successfully applies the proposed free-matrix-based integral inequality to the system with a single time-varying delay. Three numerical examples demonstrate the effectiveness of the proposed methods.

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Section: Introductionmentioning

confidence: 99%

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

2020

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“…Since the distribution characteristic of delays mentioned above has been modeled firstly as a system with two additive time-varying delay components in [4], many significant results have been devoted to this issue. As a most general form, linear systems with two additive delay components have drawn lots of attention [5][6][7][8][9][10][11][12][13][14][15]. Moreover, neural networks [16][17][18][19][20][21], T-S fuzzy systems [22,23], and Lur'e systems [24], considering two additive delay components in the state, have been also investigated recently.…”

Section: Introductionmentioning

confidence: 99%

“…A novel LKF [9] is constructed, for which positive definiteness is ensured by the whole LKF rather than each term. In [10], a delay-partitioningbased LKF was established, which greatly reduces the conservatism. In [11], a novel LKF containing delay-product type terms [12,13] is constructed; meanwhile, both the Wirtinger-based inequality [28] and reciprocally convex combination technique [33] are utilized to estimate the derivative of LKF.…”

Section: Introductionmentioning

confidence: 99%

New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Liu

2020

Complexity

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This paper focuses on the stability problems of continuous linear systems with two additive time-varying delay components. Firstly, an effective and simple Lyapunov–Krasovskii functional (LKF) is established, which not only takes adequate information of delay components and their upper bounds into consideration but also establishes a simpler form to decrease the computational complexity. Secondly, an improved delay-dependent stability criterion together with its corollary is obtained by employing the generalized free-weighting-matrix-based (GFWM-based) inequality and some other techniques to calculate the derivative of the constructed LKF, which will further reduce the introduced estimation error and make the criteria less conservative. Lastly, a numerical example is presented to illustrate the less conservatism and lower computational complexity of the derived results.

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Stability Analysis of Additive Time-Varying T–S Fuzzy System Using Augmented Lyapunov Functional

Ganesan

Manivannan

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Improved stability criterion for linear systems with two additive time-varying delay

Cited by 5 publications

References 20 publications

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Stability Analysis of Additive Time-Varying T–S Fuzzy System Using Augmented Lyapunov Functional

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