山东大学学报（理学版）
山東大學學報（理學版）
산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2007年
12期
1-9
,共9页
时滞哈密顿系统%鲁棒稳定性%充分条件%不确定性%时滞非线性系统
時滯哈密頓繫統%魯棒穩定性%充分條件%不確定性%時滯非線性繫統
시체합밀돈계통%로봉은정성%충분조건%불학정성%시체비선성계통
time-delay Hamiltonian system%robust stability%sufficient condition%uncertainty%time-delay nonlinear system
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.
研究瞭帶有時滯的哈密頓繫統的穩定性問題.針對幾類時滯哈密頓繫統,根據Lyapunov函數法併結閤哈密頓繫統的內在結構性質,提齣一些穩定性的充分條件.攷慮瞭哈密頓函數中帶有時滯的繫統的魯棒穩定性問題,在此基礎上通過哈密頓實現研究瞭一類時滯非線性繫統的穩定性.討論瞭一類不確定時滯哈密頓繫統的穩定性,這類繫統的結構矩陣含有屬于某些凸有界多項域的時不變不確定性.給齣瞭幾箇數值例子,通過例子研究錶明,所提齣的結果對于分析時滯非線性繫統的穩定性是非常有效的.
연구료대유시체적합밀돈계통적은정성문제.침대궤류시체합밀돈계통,근거Lyapunov함수법병결합합밀돈계통적내재결구성질,제출일사은정성적충분조건.고필료합밀돈함수중대유시체적계통적로봉은정성문제,재차기출상통과합밀돈실현연구료일류시체비선성계통적은정성.토론료일류불학정시체합밀돈계통적은정성,저류계통적결구구진함유속우모사철유계다항역적시불변불학정성.급출료궤개수치례자,통과례자연구표명,소제출적결과대우분석시체비선성계통적은정성시비상유효적.
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 Hamiltonian systems. First, the stability is studied for the system with delay only in the Hamiltonian function, with which the stability of a class of time-delay nonlinear systems is also investigated by Hamiltonian realization. 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.
