The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian...The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally, this paper proposes several sufficient conditions for feedback dissipative realization.展开更多
This paper Investigates Hamiltonian realization of time-varying nonlinear （TVN） systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generaliz...This paper Investigates Hamiltonian realization of time-varying nonlinear （TVN） systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is sin- gular; this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non- singular main diagonal block. Furthermore, some sufficient （necessary and sufficient） conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.展开更多
基金This work was supported by Project 973 of China(Grant Nos.G1998020307,G1998020308)China Postdoctoral Science Foundation.
文摘The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally, this paper proposes several sufficient conditions for feedback dissipative realization.
基金Supported by the National Natural Science Foundation of China (Grant No. 60474001)the Research Fund of the Doctoral Program of ChineseHigher Education (Grant No. 20040422059)the Natural Science Foundation of Shandong Province (Grant No. Y2006G10)
文摘This paper Investigates Hamiltonian realization of time-varying nonlinear （TVN） systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is sin- gular; this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non- singular main diagonal block. Furthermore, some sufficient （necessary and sufficient） conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
