The Delta-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Delta-modulation gives rise to periodic orbits. The e...The Delta-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Delta-modulation gives rise to periodic orbits. The existence of periodic points of all orders of Sigma-Delta modulation with ＂leaky＂ integration is completely characterized by some interesting groups of polynomials with ＂sign＂ coefficients. The results are naturally generalized to Sigma-Delta modulations with multiple delays, Delta-modulations in the ＂downlink＂, unbalanced Delta-modulations and systems with two-level quantized feedback. Further extensions relate to the existence of periodic points arising from Delta-modulated feedback control of a stable linear system in an arbitrary direction, for which some necessary and sufficient conditions are given.展开更多
It is well known that a shaded link diagram corresponds to a signed plane multi-graph.In graph theory,line graph is an old and important concept originally introduced by H.Whitney in 1932.In this paper we define the l...It is well known that a shaded link diagram corresponds to a signed plane multi-graph.In graph theory,line graph is an old and important concept originally introduced by H.Whitney in 1932.In this paper we define the line graph link to be a link which has a diagram whose corresponding signed plane graph is a signed line graph.The main purpose of the paper is to illustrate the structure of planar line graphs,which permits us to deal with its signed Tutte polynomial and the Jones polynomials of line graph links.展开更多
基金the National Natural Science Foundation of China (No.60674113)
文摘The Delta-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Delta-modulation gives rise to periodic orbits. The existence of periodic points of all orders of Sigma-Delta modulation with ＂leaky＂ integration is completely characterized by some interesting groups of polynomials with ＂sign＂ coefficients. The results are naturally generalized to Sigma-Delta modulations with multiple delays, Delta-modulations in the ＂downlink＂, unbalanced Delta-modulations and systems with two-level quantized feedback. Further extensions relate to the existence of periodic points arising from Delta-modulated feedback control of a stable linear system in an arbitrary direction, for which some necessary and sufficient conditions are given.
基金This paper is supported by the Fundamental Research Funds for the Central Universities(Grant No.20720190071).
文摘It is well known that a shaded link diagram corresponds to a signed plane multi-graph.In graph theory,line graph is an old and important concept originally introduced by H.Whitney in 1932.In this paper we define the line graph link to be a link which has a diagram whose corresponding signed plane graph is a signed line graph.The main purpose of the paper is to illustrate the structure of planar line graphs,which permits us to deal with its signed Tutte polynomial and the Jones polynomials of line graph links.
