几类时滞非线性哈密顿系统的稳定性分析(英文)

Stability analysis for some classes of time-delay nonlinear Hamiltonian systems

研究了带有时滞的哈密顿系统的稳定性问题。针对几类时滞哈密顿系统,根据Lyapunov函数法并结合哈密顿系统的内在结构性质,提出一些稳定性的充分条件。考虑了哈密顿函数中带有时滞的系统的鲁棒稳定性问题,在此基础上通过哈密顿实现研究了一类时滞非线性系统的稳定性。讨论了一类不确定时滞哈密顿系统的稳定性,这类系统的结构矩阵含有属于某些凸有界多项域的时不变不确定性。给出了几个数值例子,通过例子研究表明,所提出的结果对于分析时滞非线性系统的稳定性是非常有效的。

A The stability of Hamiltonian systems with time delay was investigated. Using the technique of the Lyapunov direct method and the dissipative structural properties of Hamiltonian systems, some sufficient conditions are derived for the stability of several classes of time-delay Hamihonian systems. First, the stability is studied for the system with delay only in the Hamihonian function, with which the stability of a class of time-delay nonlinear systems is also investigated by Hamiltonian reahzation. Second, the robust stability is considered for a class of time-delay Hamiltonian systems which possesse time-invariant uncertainties belonging to some convex bounded polytypic domain. Finally, several illustrative examples are studied by using the proposed results. Examples show that the results are very practicable in analyzing the stability of some classes of time-delay nonlinear systems.