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...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.展开更多
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 adde...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.展开更多
The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability condition...The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.展开更多
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 independe...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.展开更多
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 rul...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.展开更多
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...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.展开更多
This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying delays.By using vector Lyapunov function approach and linear matrix inequalities （LMIs）,new stabilit...This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying delays.By using vector Lyapunov function approach and linear matrix inequalities （LMIs）,new stability conditions are derived.These results proposed in this paper are all at subsystems level.After 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.展开更多
This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve be...This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.展开更多
This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov functional,which makes use of the information of both the lower and upper bounds of the interval time-varying...This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov 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.Furthermore,the relationship of the time-varying delay and its lower bound and upper bound is taken into account.As a result,some less conservative delay-dependent stability criteria are obtained without ignoring any useful information in the derivative of Lyapunov functional,which are established in the forms of linear matrix inequalities.Numerical examples are provided to show that the obtained results are better than existing ones.展开更多
This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities （LMIs）, less conservative delay-range-dependent stabi...This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities （LMIs）, less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.展开更多
This paper focuses on the study and the characterization of stability regions of discrete time systems with a time varying state delay subjected to actuator saturation through anti-windup strategies. Delay-dependent s...This paper focuses on the study and the characterization of stability regions of discrete time systems with a time varying state delay subjected to actuator saturation through anti-windup strategies. Delay-dependent stability conditions are stated in the local as well as global context. An optimization procedure to maximize the estimate of domain of attraction is given. The proposed technique is illustrated by means of numerical examples.展开更多
This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S） model. The main results given here focus on the stability criteria usi...This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S） model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.展开更多
This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delay-dependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with ...This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delay-dependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.展开更多
A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability crite...A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.展开更多
This paper studies the problem of stability for continuous-time systems with differentiable time-varying delays.By using the information of delay derivative,improved asymptotic stability conditions for time-delay syst...This paper studies the problem of stability for continuous-time systems with differentiable time-varying delays.By using the information of delay derivative,improved asymptotic stability conditions for time-delay systems are presented.Unlike the previous methods,the upper bound of the delay derivative is taken into consideration even if this upper bound is larger than or equal to 1.It is proved that the obtained results are less conservative than the existing ones.Meanwhile,the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved.Numerical examples are given to illustrate the effectiveness and less conservatism of the obtained stability conditions.展开更多
This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delaydependent stability condition is derived by using the novel augmented Lyapunov–Krasovskii function with ...This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delaydependent stability condition is derived by using the novel augmented Lyapunov–Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.展开更多
The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)...The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.展开更多
基金The National Natural Science Foundation of China(No.60874030,60574006,60404006)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.07KJB510125)
文摘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.
基金State Key Laboratory of Hydroscience and Engineering Under Grant No.2008-TC-2National Natural Science Foundation of China Under Grant No.90510018,50779021 and 90715041
文摘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.
基金the National Natural Science Foundation of China (69874008).
文摘The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.
基金This work was supported by the National Natural Science Foundation of China(No. 60275013).
文摘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.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘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.
基金supported by the Doctoral Startup Foundation of Taiyuan University of Science and Technology,China (Grant No. 20112010)
文摘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.
基金supported by the Postdoctoral Science Foundation of China(No.20090451275)the Scientific Research Program for the Education Department of Liaoning Province of China(No.2008017)the National Nature Science foundation of China(No.61074040)
文摘This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying delays.By using vector Lyapunov function approach and linear matrix inequalities （LMIs）,new stability conditions are derived.These results proposed in this paper are all at subsystems level.After 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.
基金supported by the National Natural Science Foundation of China(61403001,61572032)in part by the Natural Science Foundation of Anhui Province of China(1508085QF136)in part by the Natural Science Foundation of Universities of Anhui Province of China(KJ2016A058)
文摘This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.
基金supported by the National Natural Science Foundation of China (60874025)the Natural Science Foundation of Hunan Province(10JJ6098)the Scientific Research Fund of Hunan Provincial Education Department (10C0638)
文摘This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov 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.Furthermore,the relationship of the time-varying delay and its lower bound and upper bound is taken into account.As a result,some less conservative delay-dependent stability criteria are obtained without ignoring any useful information in the derivative of Lyapunov functional,which are established in the forms of linear matrix inequalities.Numerical examples are provided to show that the obtained results are better than existing ones.
文摘This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities （LMIs）, less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.
文摘This paper focuses on the study and the characterization of stability regions of discrete time systems with a time varying state delay subjected to actuator saturation through anti-windup strategies. Delay-dependent stability conditions are stated in the local as well as global context. An optimization procedure to maximize the estimate of domain of attraction is given. The proposed technique is illustrated by means of numerical examples.
文摘This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S） model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.
基金supported by the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province of China (Grant No. BS2010SF001)Research Fund for the Doctors of Binzhou University (Grant No. 2010Y09)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AM031)
文摘This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delay-dependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.
基金supported by NSFC (10871078)863 Program of China (2009AA044501)+1 种基金an Open Research Grant of the State Key Laboratory for Nonlinear Mechanics of CASGraduates' Innovation Fund of HUST (HF-08-02-2011-011)
文摘A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.
基金Program for New Century Excellent Talents in University(NCET-04-0283)the Funds for Creative Research Groups of China(60521003)+3 种基金Program for Changjiang Scholars and Innovative Research Team in University(IRT0421)the State Key Program of National Natural Science Foundation of China(60534010)National Natural Science Foundatiou of China(60674021)the Funds of Ph.D.Program of Ministry of Education,China(20060145019)
文摘This paper studies the problem of stability for continuous-time systems with differentiable time-varying delays.By using the information of delay derivative,improved asymptotic stability conditions for time-delay systems are presented.Unlike the previous methods,the upper bound of the delay derivative is taken into consideration even if this upper bound is larger than or equal to 1.It is proved that the obtained results are less conservative than the existing ones.Meanwhile,the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved.Numerical examples are given to illustrate the effectiveness and less conservatism of the obtained stability conditions.
基金Supported by National Natural Science Foundation of China（60574011）
Acknowledgement The authors would like to thank Professor YANG Guang-Hong for his guidance.
基金supported by the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province of China (Grant No. BS2010SF001)Research Fund for the Doctors of Binzhou University (Grant No. 2010Y09)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AM031)
文摘This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delaydependent stability condition is derived by using the novel augmented Lyapunov–Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.
文摘The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.
