Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two "masses" and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper...Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two "masses" and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper bound of the number of generalized Euler configurations for the cases b 1 and b = 2, 3. This paper obtains the optimal upper bound for the remaining real values of b in a systematic way.展开更多
This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time dela...This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10473025, 10833001)
文摘Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two "masses" and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper bound of the number of generalized Euler configurations for the cases b 1 and b = 2, 3. This paper obtains the optimal upper bound for the remaining real values of b in a systematic way.
基金National Natural Science Foundation of China (No.60674088)
文摘This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.
