Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

Jiang, Xiefu; Han, Qing‐Long

doi:10.1016/j.automatica.2006.02.019

Cited by 262 publications

(226 citation statements)

References 12 publications

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“…We first consider asymptotic stability for the nominal system (8). Employing Lyapunov-Krasovskii functional (9), we have the following result.…”

Section: New Stability Criteriamentioning

confidence: 99%

“…Some numerical examples will be given to show the improvement over some previous results. For any delay satisfying Case 1 or Case 2, our objective of this study is to develop new stability criteria which guarantee that system (8) is asymptotically stable and the system (8) subject to some uncertainties is robustly stable. For this purpose, the following lemmas are introduced.…”

Section: System Descriptions and Preliminariesmentioning

confidence: 99%

“…In this paper, we will study stability criteria of system described by (8) satisfying (6) or (7), employing the following new Lyapunov-Krasovskii functional:…”

Section: System Descriptions and Preliminariesmentioning

confidence: 99%

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Delay‐Dependent Stability Criteria for Systems with Interval Time‐Varying Delay

2011

Journal of Control Science and Engineering

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This paper is concerned with robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval, which means that the derivative of the time-varying delay has an upper bound or a restriction. On other occasions, if we do not take restriction on the derivative of the time-varying delay into consideration, it allows the delay to be a fast time-varying function. The uncertainty under consideration includes a polytopic-type uncertainty and a linear fractional norm-bounded uncertainty. In order to obtain much less conservative results, a new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive some new stability criteria. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria.

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“…We first consider asymptotic stability for the nominal system (8). Employing Lyapunov-Krasovskii functional (9), we have the following result.…”

Section: New Stability Criteriamentioning

confidence: 99%

Section: System Descriptions and Preliminariesmentioning

confidence: 99%

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Delay‐Dependent Stability Criteria for Systems with Interval Time‐Varying Delay

2011

Journal of Control Science and Engineering

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“…Considerable effort has been applied to different aspects of linear time-delay systems in recent years (Hale and Verduyn lunel, 1993;Huang and Zhou, 2000;Ivanesu et al, 2000;Mahmoud and AlMuthairi, 1994;Liu, 2005;Xue and Qiu, 2000;Xia and Jia, 2003). Moreover, the stability analysis of interval time-varying systems has been focused on as a topic of theoretical and practical importance (He et al, 2006;Jiang and Han, 2008;Yue, 2006;Jiang and Han, 2006;Kwon and Park, 2008). Systems with interval time-varying delays mean that the lower bound of the time delay which guarantees the stability of the system is not restricted to zero.…”

Section: Introductionmentioning

confidence: 99%

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Balasubramaniam¹,

Shanmugam²,

Rakkiyappan³

2012

International Journal of Applied Mathematics and Computer Science

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This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

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“…Thus, the stability analysis and synthesis of systems with time delay have been one of the hottest topic in control society. For recent trends of the topic, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Novel Results for Global Exponential Stability of Uncertain Systems with Interval Time-varying Delay

Liu¹,

Lee²,

Kwon³

et al. 2013

Journal of Electrical Engineering and Technology

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-This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

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Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

Cited by 262 publications

References 12 publications

Delay‐Dependent Stability Criteria for Systems with Interval Time‐Varying Delay

Delay‐Dependent Stability Criteria for Systems with Interval Time‐Varying Delay

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Novel Results for Global Exponential Stability of Uncertain Systems with Interval Time-varying Delay

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