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

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

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delay-dependent Non-fragile H_∞ Control for Linear Systems with interval time-varying delay

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International Journal of Automation and computing 2015年第1期12卷 109-116页

作者： Jun-Jun Hui He-Xin Zhang Xiang-Yu Kong The Xi'an Research Institute of High Technology

This paper considers the problem of delay-dependent non-fragile H∞control for a class of linear systems with interval time-varying delay. Based on the direct Lyapunov method, an appropriate Lyapunov-Krasovskii functional(LKF) with triple-integral terms and augment terms is introduced. Then, by using the integral inequalities and convex combination technique, an improved H∞performance analysis criterion and non-fragile H∞controller are formulated in terms of linear matrix inequalities(LMIs), which can be easily solved by using standard numerical packages. At last, two numerical examples are provided to demonstrate the effectiveness of the obtained results.

关键词： Lyapunov-Krasovskii functional(LKF) non-fragile H∞control linear matrix inequality(LMI) interval time-varying delay

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New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

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Journal of Southeast University(English Edition) 2011年第4期27卷 375-378页

作者：薛明香费树岷李涛潘俊涛东南大学复杂工程系统测量与控制教育部重点实验室南京210096 安徽大学数学科学学院合肥230601 南京航空航天大学自动化学院南京210007

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

关键词： Lurie system reciprocal convex technique absolute stability interval time-varying delay linear matrix inequality (LMI)

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Reciprocally Convex Approach to H∞ Control for Linear Systems with interval time-varying delay

Reciprocally Convex Approach to H∞ Control for Linear Syste...

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第24届中国控制与决策会议

作者： CHENG Wubin, XIAO Shenping, ZENG Hongbing, BAI Lei School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412008, China.

This paper considers less conservative results on H∞ control for linear systems with interval time-varying delay. In order to essentially improve the existing results of the system with a prescribed level γ of H ∞ disturbance attenuation, reciprocally convex approach is proposed to establish a new delay-dependent bounded real lemma （BRL）. The BRL is applied to solve the H∞ controller design by incorporating with the cone complementary minimization. A numerical example is finally given to show that the proposed method is effective and can provide less conservative results in this paper.

关键词： Reciprocally Convex Approach Stability interval time-varying delay H ∞ Control Linear Matrix Inequality (LMI)

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A Novel Stability Criterion for Systems with interval time-varying delay and Nonlinear Perturbations

A Novel Stability Criterion for Systems with Interval Time-v...

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第三十届中国控制会议

作者： YU Di,LI Fanbiao,ZHANG Xiant School of Mathematical Science,Heilongjiang University,Harbin 150080,P.R.China

＜正＞This paper focuses on the stability analysis of linear systems with interval time-varying delay and nonlinear perturbations. New stability criteria for the class of systems are obtained by combining Jensen inequality and delay dividing approach. As by-products,robust stability criterion ate presented when the lower bound of time delay is zero or the nonlinear perturbations are *** is mathematical investigated that the robust stability criteria proposed in this paper are less conservative than those in[1],and remove simultaneously the free-weighting matrices required in Zhang and Care’ *** examples show that the new method is effective than some previous approaches.

关键词： interval time-varying delay Stability Nonlinear perturbations Linear matrix inequality(LMI)

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Novel robust stability criteria for interval time-varying delay systems with nonlinear perturbations

Novel robust stability criteria for interval time-varying de...

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第30届中国控制与决策会议

作者： Yu-bin WU He-xin ZHANG Guo-liang LI Da-wei SUN Yong-qiang LI High-Tech Institute of Xi’an

In this paper, the problem of delay dependent robust stability for a class of interval time-varying delay systems with nonlinear perturbations is studied. Based on the idea of delay-partitioning method（DPM）, the whole delay interval is divided into two unequal subintervals at appropriate point and a new Lyapunov-Krasovskii functional（LKF） which contains some quadruple-integral terms and augment terms is introduced on each interval. Then, a new bounding technique based on a novel integral inequality approach together with reciprocally convex combination technique is used to deal with the cross term of the derivative. Hence, an enhanced delay-dependent stability criterion is derived in terms of linear matrix inequality（LMI）. Finally, the numerical simulation results show that the proposed method is effective and less conservative.

关键词： delay-partitioning method Lyapunov-Krasovskii functional(LKF) interval time-varying delay Quadruple-integral terms Integral inequality approach Reciprocally convex combination

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An Improved Stability Criterion for a Class of Linear Systems with interval time-varying delay

An Improved Stability Criterion for a Class of Linear System...

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第30届中国控制与决策会议

作者： Li Yao Xiefu Jiang Meichen Wang Yiwen Zhang School of Automation Hangzhou Dianzi University

In this paper, the stability problem of a class of interval time-varying delay systems is studied. By improving the Lyapunov-Krasovskii functional of the existing literatures, we introduce triple integral terms and an augmented matrix. The advantage is that we can make full use of the delay information. Wirtinger-based integral inequalities and the technique of convex combination are used to deal with the integral terms generated by the derivative of Lyapunov-Krasovskii functional and the sufficient conditions of system stability are given in the form of linear matrix inequalities（LMIs）. Finally, two examples are given to verify the validity and correctness of the results.

关键词： interval time-varying delay Wirtinger-based integral inequalities linear matrix inequalities stability criterion

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Improved delay-dependent Stability Conditions for Systems with interval time-varying delay

Improved Delay-dependent Stability Conditions for Systems wi...

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第二十九届中国控制会议

作者： GE Xiaohua1,JIANG Xiefu2 1.School of Automation,Hangzhou Dianzi University,Hangzhou 310018,P.R.China2.Research Institute of Automation,Hangzhou Dianzi University,Hangzhou 310018,P.R.China

This paper deals with the stability issues of linear systems with interval time-varying ***,two kinds of time-varying delay are ***,based on a new delay bisection approach and a tighter bounding inequality,some less conservative stability conditions are proposed,which are effective for both slow and fast time-varying *** model transformation and no slack matrix variable are ***,overly bounding for some cross term is ***,two numerical examples are given to show the effectiveness of the proposed results.

关键词： interval time-varying delay delay-dependent delay Bisection Approach Linear Matrix Inequality(LMI)

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Novel Stability Conditions for Markovian Jump Systems with interval time-varying delay

Novel Stability Conditions for Markovian Jump Systems with I...

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2011 Chinese Control and Decision Conference（CCDC）

作者： Yonggang Chen and Quanxiang Pan are with Department of Mathematics,Henan Institute of Science and Technology,Xinxiang 453003,China.Jianwei Xia is with School of Mathematic Science,Liaocheng University,Liaocheng 252000,China.

This paper investigates the robust stochastic stability analysis problem for a class of uncertain Markovian jump linear systems with interval time-varying *** employing the more general decomposition of delay interval and using the upper and lower bounds of delay-derivative,the less conservative stochastic stability and robust stochastic stability conditions are derived in terms of linear matrix inequalities （LMIs）.Numerical examples show that the proposed results improve some existing ones.

关键词： Stochastic stability Markovian jump systems interval time-varying delay Linear matrix inequalities (LMIs)

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delay-Derivative-Dependent Absolute Stability Criterion for Neutral Type Lurie System with interval time-varying delay

Delay-Derivative-Dependent Absolute Stability Criterion for ...

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第三十届中国控制会议

作者： XUE Mingxiang~(1,2),FEI Shumin~1,LI Tao~1,PAN Juntao~1 1.Key Laboratory of Measurement and Control of CSE(School of Automation,Southeast University),Ministry of Education,Nanjing 210096,Jiangsu,P.R.China 2.School of Mathematical Sciences,Anhui University,Hefei 230039,Anhui,P.R.China

＜正＞In this brief,based on Lyapunov-Krasovskii functional approach and appropriate integral inequality,some new sufficient conditions are derived to guarantee the global asymptotically stability for neutral Lurie system with interval time-varying delay,in which the improved convex combination are *** LMI-based criterion heavily depends on both the upper and lower bounds on time delay and its derivative,which is different from the existent ones and has wider application fields than some present ***,three numerical examples can illustrate the efficiency of the new method and reduced conservatism of the presented results.

关键词： Lurie control system Absolute stability interval time-varying delay Linear matrix inequality(LMI)

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