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Journal of Southeast University(English Edition) 2009年第2期25卷 213-218页

作者：于建江张侃健费树岷东南大学自动化学院南京210096 盐城师范学院信息科学与技术学院盐城224002

The problem of the stability for a class of stochastic systems with time-varying interval delay and the norm-bounded uncertainty is investigated. Utilizing the information of both the lower and the upper bounds of the interval time-varying delay, a novel Lyapunov-Krasovskii functional is constructed. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities （LMIs）, which can be easily checked by the LMI in the Matlab toolbox. Based on the Jensen integral inequality, neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because no redundant matrix is introduced. A numerical example is given to show the effectiveness and the benefits of the proposed method.

关键词： delay-dependent stability stochastic system interval delay linear matrix inequalities(LMIs)

New delay-dependent stability criterion for discrete-time recurrent neural networks with time-varying delay

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New delay-dependent stability criterion for discrete-time re...

Further Improvement on delay-dependent stability Results for Linear Systems with Time-Varying delays

2009中国控制与决策会议

作者： Xun-Lin Zhu~1,Zhanlei Shang~1 and Hong-Yong Yang~2 1.School of Computer Science and Communication Engineering,Zhengzhou University of Light Industry,Zhengzhou,Henan,450002, China 2.School of Computer Science and Technology,Ludong University,Yantai,264025,China

＜正＞This paper studies the problem of stability analysis for discrete-time recurrent neural networks（DRNNs） with time-varying *** a weak assumption on the activation functions,by defining a more general type of Lyapunov functionals and using a convex combination technique,a new delay-dependent stability criterion is proposed to guarantee the stability and uniqueness of equilibrium point of DRNNs in terms of linear matrix inequalities（LMIs）.Compared with the existing results,the newly obtained stability condition is less conservative.A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

关键词： delay-dependent stability discrete-time recurrent neural networks(DRNNs) linear matrix inequalities(LMIs) time-varying delays

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Further Improvement on Delay-Dependent Stability Results for...

delay-dependent robust stability of stochastic delay systems with Markovian switching

第三十届中国控制会议

作者： SHAO Hanyong School of Electrical and Information Automation,Qufu Normal University,Rizhao,Shandong Province 276826,P.R.China

＜正＞This paper investigates delay-dependent stability for linear systems with time-varying delays.A new delay-dependent stability criterion is derived by constructing a Lyapuonv functional and computing a tighter upper bound for the derivative of the Lyapuonv *** is shown that the stability criterion is less conservative than some recently reported *** examples are given to demonstrate the reduced conservatism of the proposed stability results.

关键词： Time-varying delay delay-dependent stability Lyapunov functional

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控制理论与应用（英文版） 2009年第4期7卷 367-372页

作者： Lirong HUANG Xuerong MAO Feiqi DENG Department of Mathematics and Statistics University of Strathclyde Glasgow G1 1XH UK College of Automation Science and Engineering South China University of Technology Guangzhou Guangdong 510641 China

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

关键词： Stochastic systems Time delay Markovian switching delay-dependent stability

Theoretical and experimental studies on critical time delay of multi-DOF real-time hybrid simulation

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Earthquake Engineering and Engineering Vibration 2022年第1期21卷 117-134页

作者： Lu Liqiao Wang Jinting Ding Hao Zhu Fei State Key Laboratory of Hydroscience and Engineering Tsinghua UniversityBeijing 100084China China Huaneng Group Co. Ltd.Beijing 100031China Hisense Group Co. Ltd.Qingdao 266520China

This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discrete-time root locus(RL)techniques,respectively.A bilinear transform is introduced into the first-order Padéapproximation while conducting the discrete RL *** on this technique,the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be ***,the critical time delays calculated by the continuous-and discrete-time RL techniques,respectively,are compared for a 2-DOF RTHS *** is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time ***,theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS *** analysis provides a glimpse of the effects of time step,frequency and damping ratio in a performing partitioning *** constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance,therefore facilitating successful RTHS.

关键词： real-time hybrid simulation root locus critical time delay delay-dependent stability

stability Analysis of Cyber-Physical Micro Grid Load Frequency Control System with Time-Varying delay and Non-Linear Load Perturbations

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Computer Modeling in Engineering & Sciences 2019年第12期121卷 801-813页

作者： D.Vijeswaran V.Manikandan Department of Electrical and Electronics Engineering Coimbatore Institute of TechnologyCoimbatore 641014India 不详

In a cyber-physical micro-grid system,wherein the control functions are executed through open communication channel,stability is an important issue owing to the factors related to the time-delay encountered in the data *** of feedback variable as discrete data packets in communication network invariably introduces inevitable time-delays in closed loop control *** delay,depending upon the network traffic condition,inherits a time-varying characteristic;nevertheless,it adversely impacts the system performance and *** load perturbations in a micro-grid system are considerably influenced by the presence of fluctuating power generators like wind and solar *** these non-conventional energy sources are integrated into the power grid through power electronic interface circuits that usually works at high switching frequency,noise signals are introduced into the micro-grid system and these signals gets super-imposed to the load *** on this back ground,in this paper,the delay-dependent stability issue of networked micro-grid system combined with time-varying feedback loop delay and uncertain load perturbations is investigated,and a deeper insight has been presented to infer the impact of time-delay on the variations in the system *** classical Lyapunov-Krasovskii method is employed to address the problem,and using a standard benchmark micro-grid system,and the proposed stability criterion is validated.

关键词： delay-dependent stability time-varying delay open communication network nonlinear perturbations Lyapunov-Krasovskii functional linear Matrix Inequality(LMI)

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

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Chinese Physics B 2011年第4期20卷 16-26页

作者： S.Lakshmanan P.Balasubramaniam Department of Mathematics Gandhigram Rural University

This paper studies the problem of linear matrix inequality （LMI） approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

关键词： delay-dependent stability linear matrix inequality Lyapunov-Krasovskii functional stochastic neural networks

delay-dependent TREATMENT OF LINEAR MULTISTEP METHODS FOR NEUTRAL delay DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2003年第4期21卷 535-544页

作者： SyedKhalidJaffer Ming-zhuLiu InstituteofNuclearPower P.Box3140IslamabadPakistan DepartmentofMathematics HarbinInstituteofTechnologyHarbin150001China

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations y'(t) = ay(t) + by(t - τ) + cy'(t - τ), t > 0, y(t) = g(t), -τ≤ t ≤ 0, a,b andc ∈ R. The necessary condition for linear multistep methods to be Nτ(0)-stable is given. It is shown that the trapezoidal rule is Nτ(0)-compatible. Figures of stability region for some linear multistep methods are depicted.

关键词： delay-dependent stability Linear multistep methods Neutral delay differential equations.

An improved robust stability analysis for systems with two delays by extracting overlapping feature

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Journal of Control and Decision 2015年第2期2卷 124-141页

作者： Dushmanta K.Das Sandip Ghosh Bidyadhar Subudhi Department of Electrical and Electronics Engineering National Institute of Technology NagalandDimapurIndia Department of Electrical Engineering National Institute of Technology RourkelaRourkelaIndia

In this paper,a delay-dependent robust stability criterion is proposed for linear systems with two *** delay-dependent stable systems,the delays are very small in ***,they may overlap each *** overlapping information may be exploited to obtain a less conservative *** extract such information,a special type of simple Lyapunov–Krasovskii functional is *** derive the criterion in form of Linear Matrix inequalities,a matrix variable approach is *** numerical examples are presented to validate the less conservativeness of the proposed criterion.

关键词： time-delay system Lyapunov-Krasovskii functional delay-dependent stability