The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that ...The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator’s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real right-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.展开更多
In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the loca...In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.展开更多
Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the...Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.展开更多
基金This work was supported by the National Natural Science Foundation(No.60274007)the Doctoral Foundation of Education Ministry(No.20010487005)the Academic Foundation of Naval University of Engineering(No.E988).
文摘The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator’s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real right-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.
基金supported by National Natural Science Foundation of China (Grant No. 11571128)
文摘In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.
基金Project supported by the Talent Introduction Foundation of Qiannan Normal University of Nationalities,China(Grant No.qnsyrc201619)Natural Science Foundation of Guizhou Provincial Education Department for Young Talents,China(Grant No.Qian Education Contract KY[2017]339)Chemical Sciences,Geosciences and Biosciences Division,Office of Basic Energy Sciences,Office of Science,U.S.Department of Energy(Grant No.DE-FG02-86ER13491)
文摘Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.
