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delay-dependent criteria for the robust stability of systems with time-varying delay

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控制理论与应用（英文版） 2003年第1期1卷 97-100页

作者： MinWU YongHE JinhuaSHE SchoolofInformationScienceandEngineenng CenwalSouthUniversityChangshaHunan410083China DeparmaentofMechatronics TokyoUmversiWofTechinologyTokyo192-0982Japan

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach. Keywords delay-dependent criteria - Robust stability - Time-varying structured uncertainties - Nonlinear perturbations - Linear matrix inequality This work was supported by the Doctor Subject Foundation of China (No. 2000053303).

关键词： delay-dependent criteria Robust stability Time-varying structured uncertainties Nonlinear perturbations Linear matrix inequality

delay-dependent Stability criteria for Uncertain Neutral Systems

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Delay-dependent Stability Criteria for Uncertain Neutral Sys...

delay-dependent Stability criteria for Systems with Multiple delays

2010 Chinese Control and Decision Conference

作者： Chang Liu,Zhaodi Xu,Guangxin Zhong 1.School of Mathematics and System Science,Shenyang Normal University,Shenyang,110034

In this paper,the problem of delay-dependent stability criteria for a class of constant time-delay neutral systems with time-varying structured uncertainties is *** using Lyapunov-Krasovskii functional that splits the whole delay interval into two subintervals and defines different Lyapunov function on each subinterval,The asymptotic stability criteria and robustly stability criteria are presented in terms of strict linear matrix inequalities (LMIs).Two numerical examples are given to indicate that the results presented in this paper are effective and less conservative than some existing results.

关键词： Neutral systems delay-dependent criteria uncertainty linear matrix inequality(LMI)

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Delay-dependent Stability Criteria for Systems with Multiple...

delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

第二十三届中国控制会议

作者： Wu Min, Zhu Shi-Peng, He Yong School of Information Science and Engineering, Central South University, Changsha 410083,China

＜正＞ This paper focus on the problem of the delay-dependent stability of linear systems with multiple time-delays. A new method is first presented for the systems with two time-delays, in which some free-weighting matrices are given to express the relationships between the terms in the Leibniz-Newton formula. In addition, the equivalence between the systems with two identical time-delays and the systems with single delay is shown, which overcomes the conservatism of the previous results. Next, a numerical example is used to demonstrate that the criteria given in this paper are effective and are a significant improvement over existing ones. Finally, the basic idea is extended to a system with multiple time delays.

关键词： delay-dependent criteria stability linear matrix inequality multiple delay.

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控制理论与应用（英文版） 2009年第3期7卷 291-296页

作者： Yumei LI Xinping GUAN Dan PENG Changchun HUA Xiaoyuan LUO Institute of Mathematics and System Science Xinjiang University Urumuqi Xinjiang 830046 China Institute of Electrical Engineering Yanshan University Qinhuangdao Hebei 066004 China

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.

关键词： Stochastic system Exponential stability in mean square Time-varying state delay delay-dependent criteria Linear matrix inequality (LMI)

On delay-dependent robust stability for uncertain neutral systems

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Journal of Systems Engineering and Electronics 2005年第2期16卷 351-355页

作者： HeYong WuMin SchoolofInformationScienceandEngineering CentralSouthUniversityChangsha410083P.R.China//SchoolofMathematicalScienceandComputingTechnologyCentralSouthUniversityChangsha410083P.R.China SchoolofInformationScienceandEngineering CentralSouthUniversityChangsha410083P.R.China

The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.

关键词： neutral system delay-dependent criteria robust stability time-varying structured uncertainties linear matrix inequality.

Integral-inequality approach to delay-dependent robust H-infinity control for uncertain neutral systems

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控制理论与应用（英文版） 2008年第2期6卷 208-214页

作者： Wen＇an ZHANG Li YU Department of Automation Zhejiang University of Technology Hangzhou Zhejiang 310032 China

This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bounded real lemma for such systems is derived without involving a fixed model transformation. Furthermore, new delay-dependent sufficient conditions for the existence of robust H-infinity controllers are presented in terms of nonlinear matrix inequalities. A design procedure involving an iterative algorithm is also proposed to design such controllers. Numerical examples are given to demonstrate the less conservatism of the proposed method.

关键词： Neutral systems Uncertain systems delay-dependent criteria H-infinity control Integral-inequality

A delay-dependent passivity criterion of linear neutral delay systems

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控制理论与应用（英文版） 2006年第2期4卷 201-206页

作者： Weihua GUI Biyu LIU Zhaohui TANG School of Information Science and Engineering Central South University Changsha Hunan 410083 China

The problem of delay-dependent stability and passivity for linear neutral systems is discussed. By constructing a novel type Lyapunov-krasovskii functional, a new delay-dependent passivity criterion is presented in terms of linear matrix inequalities （LMIs）. Model transformation, bounding for cross terms and selecting free weighting matrices [12-14] are not required in the arguments. Numerical examples show that the proposed criteria are available and less conservative than existing results .

关键词： Neutral delay systems delay-dependent criteria Linear matrix inequalities (LMIs) Lyapunov-krasovskii functional

delay-dependent robust stability for neutral systems with mixed discrete-and-neutral delays

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控制理论与应用（英文版） 2004年第4期2卷 386-392页

作者： YongHE MinWU JinhuaSHE SchoolofInformationScienceandErtgmeering CentralSouthUniversityChangshaHunan410083China／／SchoolofMathematicalScienceandComputingTechnologyCentralSouthUniversityChangshaHunan410083China SchoolofInformationScienceandErtgmeering CentralSouthUniversityChangshaHunan410083China DepartmentofMechatronics TokyoUniversityofTechnologyTokyo192-0982Japan

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases. A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.

关键词： Neutral system delay-dependent criteria Robust stability Time-varying structured uncertainties Linear matrix inequality

On delay-dependent robust stability of neutral systems

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控制理论与应用（英文版） 2006年第2期4卷 181-186页

作者： Renxin ZHONG Zhi YANG Guoli WANG Department of Automation and Computer-Aided Engineering The Chinese University of Hong Kong Shatin NT Hong Kong China Department of Electronics and Communication Engineering Sun Yat-Sen University Guangzhou Guangdong 510275 China

The delay-dependent robust stability of uncertain linear neutral systems with delays is investigated. Both discrete-delay-dependent/neutral-delay-independent and neutral-/discrete- delay-dependent stability criteria will be developed. The proposed stability criteria are formulated in the form of linear matrix inequalities and it is easy to check the robust stability of the considered systems. By introducing certain Lyapunov-Krasovskii functional the mathematical development of our result avoids model transformation and bounding for cross terms, which lead to conservatism. Finally, numerical example is given to indicate the improvement over some existing results.

关键词： Neutral system delay-dependent criteria Robust stability Time-varying parameter uncertainty Linear matrix inequality