In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefu...In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.展开更多
In this paper we obtain new criteria for the positive equilibrium K of thenonautonomous Hutchinson's equationN'(t) = r(t)N(t)[1-[N(t-τ)]/K], t≥0,to be uniformly stable. Examples illustrating the significance...In this paper we obtain new criteria for the positive equilibrium K of thenonautonomous Hutchinson's equationN'(t) = r(t)N(t)[1-[N(t-τ)]/K], t≥0,to be uniformly stable. Examples illustrating the significance of the results arealso given.展开更多
Distinctness, Uniformity and Stability （DUS） testing is the technical base of Plant Variety Protection （PVP） and the scientific basis for the approval of Plant Breeder＇s Rights （PBR）. DUS Test Guidelines are no...Distinctness, Uniformity and Stability （DUS） testing is the technical base of Plant Variety Protection （PVP） and the scientific basis for the approval of Plant Breeder＇s Rights （PBR）. DUS Test Guidelines are not only the technical manuals for the DUS testing authorities to conduct the testing, but also the technical standards for the competent authorities to examine the DUS of new varieties of plants. Tea plant, originated from Yunnan Province, China, is a very important woody cash species in the world. The International Union for the Protection of New Varieties of Plants （UPOV） DUS Test Guidelines for tea plant is the first Test Guidelines prepared by China for the UPOV. In this article, the subject, selection, and determination of characteristics, states of expression of characteristics and the selection of example varieties, assessment of the UPOV DUS Test Guidelines for tea plant were elucidated in detail. Finally, the proposal of PVP for tea plant in China was also proposed. The preparation of UPOV DUS Test Guidelines for tea plant will have important significance both for promoting the development of PVP and increasing the status of international PVP fields for China.展开更多
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theo...In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.展开更多
In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the w...In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.展开更多
In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero soluti...In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.展开更多
This paper obtained some theorems that can ascertain the zero solution of functional differential equations are extremely uniformly stable, extremely asymptotically stable or extremely uniformly asymptotically stable....This paper obtained some theorems that can ascertain the zero solution of functional differential equations are extremely uniformly stable, extremely asymptotically stable or extremely uniformly asymptotically stable. In the obtained theorems, the derivative of Liapunov function on t along the solutions of functional differential equations is not required to be always negative, especially, it may be even positive.展开更多
The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second metho...The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second method. The obtained conclusions generalize some results of Stability of Equation (x)(t)+p(t)(x)(t)+q(t)x(t)=0 and Jack Hale in his paper of Theory of Functional Differential Equations.展开更多
In this paper, stability problems for the second order nonlinear differential equations disturbed with delays are studied. By means of the new stability theorems and Liapunov functional, the authors obtain some result...In this paper, stability problems for the second order nonlinear differential equations disturbed with delays are studied. By means of the new stability theorems and Liapunov functional, the authors obtain some results of the zero solution of the equations, some well-known results are extended.展开更多
In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore,...In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.展开更多
The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the su...The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.展开更多
An improved Narendra model reference adaptive control (MRAC) scheme isproposed to research one variable displacement pump driving four hydraulic variable displacementmotors. This approach not only ensures the underdam...An improved Narendra model reference adaptive control (MRAC) scheme isproposed to research one variable displacement pump driving four hydraulic variable displacementmotors. This approach not only ensures the underdamped and unstable system be global uniformasymptotic stability, but also has good robustness in these aspects of modeling uncertainty,pressure fluctuation of constant pressure network, and disturbance from external load, which alsoupgrades the rapidity of system response so as to make controlled system with nicer dynamic quality.The scheme of one pump driving four motors can meet the demand on off-road mobility of engineeringvehicles and armored cars. A proof of stability about improved Narendra MRAC scheme is also given.展开更多
Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines wh...Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines originally proposed by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper.展开更多
In this paper. we prove the existence of the global classical solutions and the uniform stability of the zero solution to the initial value problem for a class of high dimensional dynamic systems which contain the deg...In this paper. we prove the existence of the global classical solutions and the uniform stability of the zero solution to the initial value problem for a class of high dimensional dynamic systems which contain the degenerate case.展开更多
One-dimensional differential equations of the form x'(t) + λx(t) = F(t, xt) areconsidered assuming that λ> 0 and that F satisfies either -or a condition in which N is replaced by M, wheremax, and μis bounded...One-dimensional differential equations of the form x'(t) + λx(t) = F(t, xt) areconsidered assuming that λ> 0 and that F satisfies either -or a condition in which N is replaced by M, wheremax, and μis bounded, nondecre-asing and is left continuous on [0, ∞], we obtain sufficient conditions for theuniform stability and uniformly asymptotic stability of the zero solution of theequation, the results in paper [7] are improved.展开更多
This paper presents a discussion of differential equations with two terms generated by delays. They are as follows x′(t) = a(t)x(t - p(t)) - b(t)x(t - r(t)).Sufficient conditions for its solution with uniform bound a...This paper presents a discussion of differential equations with two terms generated by delays. They are as follows x′(t) = a(t)x(t - p(t)) - b(t)x(t - r(t)).Sufficient conditions for its solution with uniform bound and for its zero solution with uniform stability are established.展开更多
This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial ...This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.展开更多
基金The work of both authors was partially supported by the Center for Computational Mathematics and ApplicationsThe Pennsylvania State University,and was partially supported by NSF grant DMS-1522615.
文摘In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.
基金This project was supported by TRATOYT of P. R. China and by Trans-Century Training Programme Foundation for the Talents by the State Education Commission
文摘In this paper we obtain new criteria for the positive equilibrium K of thenonautonomous Hutchinson's equationN'(t) = r(t)N(t)[1-[N(t-τ)]/K], t≥0,to be uniformly stable. Examples illustrating the significance of the results arealso given.
文摘Distinctness, Uniformity and Stability （DUS） testing is the technical base of Plant Variety Protection （PVP） and the scientific basis for the approval of Plant Breeder＇s Rights （PBR）. DUS Test Guidelines are not only the technical manuals for the DUS testing authorities to conduct the testing, but also the technical standards for the competent authorities to examine the DUS of new varieties of plants. Tea plant, originated from Yunnan Province, China, is a very important woody cash species in the world. The International Union for the Protection of New Varieties of Plants （UPOV） DUS Test Guidelines for tea plant is the first Test Guidelines prepared by China for the UPOV. In this article, the subject, selection, and determination of characteristics, states of expression of characteristics and the selection of example varieties, assessment of the UPOV DUS Test Guidelines for tea plant were elucidated in detail. Finally, the proposal of PVP for tea plant in China was also proposed. The preparation of UPOV DUS Test Guidelines for tea plant will have important significance both for promoting the development of PVP and increasing the status of international PVP fields for China.
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
文摘In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.
文摘In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.
文摘In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.
基金National Natural Science Foundation ofChina( No.1983 10 3 0 )
文摘This paper obtained some theorems that can ascertain the zero solution of functional differential equations are extremely uniformly stable, extremely asymptotically stable or extremely uniformly asymptotically stable. In the obtained theorems, the derivative of Liapunov function on t along the solutions of functional differential equations is not required to be always negative, especially, it may be even positive.
文摘The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second method. The obtained conclusions generalize some results of Stability of Equation (x)(t)+p(t)(x)(t)+q(t)x(t)=0 and Jack Hale in his paper of Theory of Functional Differential Equations.
文摘In this paper, stability problems for the second order nonlinear differential equations disturbed with delays are studied. By means of the new stability theorems and Liapunov functional, the authors obtain some results of the zero solution of the equations, some well-known results are extended.
文摘In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.
基金supported by Hi-Tech Research and Development (863) Program of China (No.2006AA04Z207)Research Fund for Doctorial Programof Higher Education of China (No.20060006018)+1 种基金International Cooperation Program of Science and Technology of China (No.2007DFA11530)the National Natural Science Foundation of China (No.60875072)
文摘The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.
文摘An improved Narendra model reference adaptive control (MRAC) scheme isproposed to research one variable displacement pump driving four hydraulic variable displacementmotors. This approach not only ensures the underdamped and unstable system be global uniformasymptotic stability, but also has good robustness in these aspects of modeling uncertainty,pressure fluctuation of constant pressure network, and disturbance from external load, which alsoupgrades the rapidity of system response so as to make controlled system with nicer dynamic quality.The scheme of one pump driving four motors can meet the demand on off-road mobility of engineeringvehicles and armored cars. A proof of stability about improved Narendra MRAC scheme is also given.
基金Supported in part by the Specialized Research Fund for the Doctoral Program of Higher Education under grant 20060512001.
文摘Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines originally proposed by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper.
文摘In this paper. we prove the existence of the global classical solutions and the uniform stability of the zero solution to the initial value problem for a class of high dimensional dynamic systems which contain the degenerate case.
文摘One-dimensional differential equations of the form x'(t) + λx(t) = F(t, xt) areconsidered assuming that λ> 0 and that F satisfies either -or a condition in which N is replaced by M, wheremax, and μis bounded, nondecre-asing and is left continuous on [0, ∞], we obtain sufficient conditions for theuniform stability and uniformly asymptotic stability of the zero solution of theequation, the results in paper [7] are improved.
文摘This paper presents a discussion of differential equations with two terms generated by delays. They are as follows x′(t) = a(t)x(t - p(t)) - b(t)x(t - r(t)).Sufficient conditions for its solution with uniform bound and for its zero solution with uniform stability are established.
文摘This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
