The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global expo...The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique,...A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.展开更多
This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in ...This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.展开更多
The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average d...The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.展开更多
In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global e...In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.展开更多
In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique whe...In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.展开更多
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multipli...This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.展开更多
In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new...In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.展开更多
In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are e...In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.展开更多
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth conditio...The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponentially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.展开更多
A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstabl...A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstable subsystems, which not only involves state delay and norm-bounded time-varying parameter uncertainties, but also contains the impulsive switching effects between the subsystems. Based on the extension of the system dimension and the concept of average dwell time, a kind of practically useful switching rule is presented which guarantees the desired robust exponential stability. A switched state feedback controller is also given.展开更多
This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality ...This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.展开更多
This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constan...This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.展开更多
This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point,...This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.展开更多
This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, som...This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.展开更多
A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasov...A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.展开更多
This paper proposes a method for the stability analysis of deterministic switched systems.Two motivational examples are introduced (nonholonomic system and constrained pendulum).The finite collection of models consi...This paper proposes a method for the stability analysis of deterministic switched systems.Two motivational examples are introduced (nonholonomic system and constrained pendulum).The finite collection of models consists of nonlinear models,and a switching sequence is arbitrary.It is supposed that there is no jump in the state at switching instants,and there is no Zeno behavior,i.e.,there is a finite number of switches on every bounded interval.For the analysis of deterministic switched systems,the multiple Lyapunov functions are used,and the global exponential stability is proved.The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.展开更多
By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural ...By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.展开更多
文摘The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
基金Supported by the Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institutethe Younger Foundation of Yantai University (SX06Z9)
文摘A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.
基金supported by the National Natural Science Foundation of China(61673198)the Provincial Natural Science Foundation of Liaoning Province(20180550473)
文摘This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.
基金the National Natural Science Foundation of China (60674027, 60574007)Doctoral Foundation of Education Ministry of China (20050446001).
文摘The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.
基金supported by 973 Programs (No.2008CB317110)the Key Project of Chinese Ministry of Education (No.107098)+1 种基金Sichuan Province Project for Applied Basic Research (No.2008JY0052)the Project for Academic Leader and Group of UESTC
文摘In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.
基金supported by National Natural Science Foundation of China (No.60674027,No.60974127)Key Project of Education Ministry of China (No.208074)
文摘In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.
文摘Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
基金Sponsored by the NNSF of China(11031003,11271066,11326158)a grant of Shanghai Education Commission(13ZZ048)Chinese Universities Scientific Fund(CUSF-DH-D-2013068)
文摘This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.
基金Natural Science Foundation of Henan Education Department (No.2007120005).
文摘In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.
文摘In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
基金support from the National Natural Science Foundation of China(70871046,71171091,71191091)Fundamental Research Funds for the Central Universities(2011QN167)
文摘The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponentially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.
基金the National Natural Science Foundation of China(No.60674027)China Postdoctoral Science Foundation(No.20070410336)the Postdoctor Foundation of Jiangsu Province(No.0602042B).
文摘A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstable subsystems, which not only involves state delay and norm-bounded time-varying parameter uncertainties, but also contains the impulsive switching effects between the subsystems. Based on the extension of the system dimension and the concept of average dwell time, a kind of practically useful switching rule is presented which guarantees the desired robust exponential stability. A switched state feedback controller is also given.
基金supported by Natural Science Foundation of Jiangsu Province of China(No.BK2007016)Scientific Research and Development Program of the Higher Education Institutions of Shandong Province of China(No.J09LG58)
文摘This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China (No.60574001)Program for New Century Excellent Talents in University (No.050485)Program for Innovative Research Team of Jiangnan University
文摘This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
基金Project supported by the National Natural Science Foundations of China(Grant No.70871056)the Society Science Foundation from Ministry of Education of China(Grant No.08JA790057)the Advanced Talents'Foundation and Student's Foundation of Jiangsu University,China(Grant Nos.07JDG054 and 07A075)
文摘This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.
基金supported by National Natural Science Foundation of China (Grant No 60674026)the Jiangsu Provincial Natural Science Foundation of China (Grant No BK2007016)Program for Innovative Research Team of Jiangnan University of China
文摘This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.
基金This project was supported in part by the National Natural Science Foundation of China (60404022, 60604004)the Key Scientific Research project of Education Ministry of China (204014)the National Natural Science Foundation of China for Distinguished Young Scholars (60525303).
文摘A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.
基金supported by the Ministry of Science and Technological Development of the Republic of Serbia (No. TR-3326)
文摘This paper proposes a method for the stability analysis of deterministic switched systems.Two motivational examples are introduced (nonholonomic system and constrained pendulum).The finite collection of models consists of nonlinear models,and a switching sequence is arbitrary.It is supposed that there is no jump in the state at switching instants,and there is no Zeno behavior,i.e.,there is a finite number of switches on every bounded interval.For the analysis of deterministic switched systems,the multiple Lyapunov functions are used,and the global exponential stability is proved.The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.
基金The Soft Project (B30145) of Science and Technology of Hunan Province.
文摘By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.