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delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

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Earthquake Engineering and Engineering Vibration 2010年第3期9卷 425-438页

作者： Chi Fudong Wang Jinting Jin Feng State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

关键词： real-time dynamic hybrid testing root locus analysis delay-dependent stability Pade approximation added damping

delay-dependent stability of linear multistep methods for differential systems with distributed delays

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Applied Mathematics and Mechanics(English Edition) 2018年第12期39卷 1837-1844页

作者： Yanpei WANG Yuhao CONG Guangda HU Department of Mathematics College of SciencesShanghai UniversityShanghai 200444China Shanghai Customs College Shanghai 201204China

This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

关键词： differential system with distributed delays delay-dependent stability linear multistep method argument principle

delay-dependent stability Analysis of Multistep Methods for delay Differential Equations

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 607-616页

作者： Cheng-ming Huang Yang-zi Hu Hong-jiong Tian School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Department of Mathematics Shanghai Normal University Division of Computational Science E-Institute of Shanghai Universities Scientific Computing Key Laboratory of Shanghai Universities Shanghai 200234 China

This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.

关键词： delay differential equations delay-dependent stability asymptotic stability ^-(O)-stability linearmultistep methods general linear methods

delay-dependent stability of discrete-time interconnected systems

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控制理论与应用（英文版） 2010年第4期8卷 464-470页

作者： Xiaoheng CHANG Guosheng TIAN Xunlin ZHU College of Information Science and Engineering Northeastern University Shenyang Liaoning 110004 China College of Information Science and Engineering Bohai University Jinzhou Liaoning 121003 China Faculty of Electrical and Control Engineering Liaoning Technical University Huludao Liaoning 125105 China School of Computer Science and Communication Engineering Zhengzhou University of Light Industry Zhengzhou Henan 450002 China

This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying *** using vector Lyapunov function approach and linear matrix inequalities （LMIs）,new stability conditions are *** results proposed in this paper are all at subsystems *** comparing with the existing results,it is shown that these conditions are less conservative.A numerical example is presented to demonstrate the effectiveness of the results.

关键词： Interconnected systems delay-dependent stability Discrete-time LMIs

Novel delay-dependent stability criteria for neural networks with interval time-varying delay

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Chinese Physics B 2011年第12期20卷 174-180页

作者：王健安 School of Electronics Information Engineering Taiyuan University of Science and Technology

The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.

关键词： neural networks interval time-varying delay delay-dependent stability convex combi-nation linear matrix inequality

delay-dependent stability and stabilization criteria of networked control systems with multiple time-delays

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控制理论与应用（英文版） 2006年第4期4卷 321-326页

作者： Huaicheng YAN Xinhan HUANG Min WANG Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan Hubei 430074 China.

This paper deals with the problem of delay-dependent stability and stabilization for networked control systems（NCSs）with multiple time-delays. In view of multi-input and multi-output（MIMO） NCSs with many independent sensors and actuators, a continuous time model with distributed time-delays is proposed. Utilizing the Lyapunov stability theory combined with linear matrix inequalities（LMIs） techniques, some new delay-dependent stability criteria for NCSs in terms of generalized Lyapunov matrix equation and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs. Compared with the reported methods, the proposed methods give a less conservative delay bound and more general results. Numerical example and simulation show that the methods are less conservative and more effective.

关键词： Networked control systems(NCSs) delay-dependent stability Generalized Lyapunov matrix equation Linear matrix inequalities (LMIs) Networked-induced delay Maximum allowable delay bound(MADB)

delay-dependent stability Analysis and Stabilization for T-S Fuzzy Models With Time-delay

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Delay-dependent Stability Analysis and Stabilization for T-S...

delay-dependent stability of Uncertain Distributed Time-delay Systems

第二十九届中国控制会议

作者： XU Yunli,SHEN Yanjun College of Science,China Three Gorges University,Yichang 443002,P.R.China

This paper proposed new generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy time-delay *** the literature,both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been ***,those conditions are rather conservative and do not guarantee a wide stability *** we choose a generalized Lyapunov-Krasovskii functional and introduce a parameterized model transformation with free weighting matrices to it,in order to obtain generalized delay-dependent stability *** delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities（LMIs）.Comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability *** also give example to illustrate our results,and the simulation results show that the LMI conditions based on the fuzzy Lyapunov function are less conservative than those based on a common（standard）Lyapunov function.

关键词： T-S Fuzzy Systems Time-delay delay-dependent stability

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Delay-dependent Stability of Uncertain Distributed Time-dela...

New delay-dependent stability of Uncertain Discrete-Time Switched Systems with Time-Varying delays

2012 3rd International Conference on Information Technology for Manufacturing Systems(ITMS 2012)

作者： Cheng Wang Qing Zhang Jianping Gan College of Mathematics and Computer Science Huanggang Normal University Institute of Demographic Ecology and Resources Management Huanggang Normal University

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality(LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

关键词： delay-dependent stability time-delay linear matrix inequality(LMI)

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Journal of Mathematical Research and Exposition 2011年第2期31卷 224-232页

作者： Liang Lin XIONG 1,2,Shou Ming ZHONG 2,3,Mao YE 4 1.School of Mathematics and Computer Science,Yunnan Nationalities University,Yunnan 650031,P.R.China 2.School of Applied Mathematics,University of Electronic Science and Technology of China,Sichuan 610054,P.R.China 3.Key Laboratory for NeuroInformation of Ministry of Education,University of Electronic Science and Technology of China,Sichuan 610054,P.R.China 4.School of Computer Science and Engineering,University of Electronic Science and Technology of China,Sichuan 610054,P.R.China School of Mathematics and Computer Science Yunnan Nationalities University Yunnan 650031 School of Applied Mathematics University of Electronic Science and Technology of China Key Laboratory for Neurolnformation of Ministry of Education Sichuan 610054 School of Computer Science and Engineering University of Electronic Science and Technology of China Sichuan 610054

This paper deals with the issues of robust stability for uncertain discrete-time switched systems with mode-dependent time *** on a novel difference inequality and a switched Lyapunov function,new delay-dependent stability criteria are formulated in terms of linear matrix inequalities （LMIs） which are not contained in known literature.A numerical example is given to demonstrate that the proposed criteria improves some existing results significantly with much less computational effort.

关键词： discrete-time switched system difference inequality switched Lyapunov function delay-dependent stability linear matrix inequality (LMI)