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|Title:||On Hamiltonian realization of time-varying nonlinear systems|
Dissipative Hamiltonian realization
Generalized Hamiltonian realization
|Citation:||Wang, Y., Ge, S.S., Cheng, D. (2007-10). On Hamiltonian realization of time-varying nonlinear systems. Science in China, Series F: Information Sciences 50 (5) : 671-685. ScholarBank@NUS Repository. https://doi.org/10.1007/s11432-007-0041-6|
|Abstract:||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 Jacobian 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 singular, 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. © 2007 Science in China Press.|
|Source Title:||Science in China, Series F: Information Sciences|
|Appears in Collections:||Staff Publications|
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