The delay systemx·(t)=Ax(t)+Bx(t-r)is considered. The necessary and sufficient conditions of the existence of a kind of Liapunov functional for the system are given.
Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems...Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems to some nonlinear differential systems with infinite delay are discussed.展开更多
In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria ar...In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria are in concise forms, easily checked and applicable.展开更多
It is well known,that in the theory of stability in differential equations,Liapunov's second method may be the most important The center problem of Liapunov's second method is construction of Liapunov function...It is well known,that in the theory of stability in differential equations,Liapunov's second method may be the most important The center problem of Liapunov's second method is construction of Liapunov function for concrete problems.Beyond any doubt,construction of Liapunov functions is an art.In the case of functional differential equations,there were also many attempts to establish various kinds of Liapunov type theorems.Recently Burton[2]presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However,the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton,we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability.Those criteria improve the result of literature[1]and they are with simple forms,easily checked and applicable.展开更多
This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e f...This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semi--definite derivative (i.e. V≤0).展开更多
文摘The delay systemx·(t)=Ax(t)+Bx(t-r)is considered. The necessary and sufficient conditions of the existence of a kind of Liapunov functional for the system are given.
基金Project supported by the National Science Foundation of China Under Grants 69871005
文摘Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems to some nonlinear differential systems with infinite delay are discussed.
文摘In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria are in concise forms, easily checked and applicable.
基金This project is supported by the National Natural Science Foundation of China
文摘It is well known,that in the theory of stability in differential equations,Liapunov's second method may be the most important The center problem of Liapunov's second method is construction of Liapunov function for concrete problems.Beyond any doubt,construction of Liapunov functions is an art.In the case of functional differential equations,there were also many attempts to establish various kinds of Liapunov type theorems.Recently Burton[2]presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However,the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton,we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability.Those criteria improve the result of literature[1]and they are with simple forms,easily checked and applicable.
文摘This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semi--definite derivative (i.e. V≤0).
