As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the applicatio...As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform （including 3 main types： linear combination-type; sampling-type; and eigen decomposition-type）, and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.展开更多
A novel neural network model, termed the discrete-time delayed standard neural network model （DDSNNM）, and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analy...A novel neural network model, termed the discrete-time delayed standard neural network model （DDSNNM）, and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks （RNNs） and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed （or non-delayed） nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks （CNNs） and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.展开更多
This paper analyzes a queue mode] of the polling system with limited service (K=1) in discrete time. By the imbedded Markov chain theory and the probability generating function method, the mean values of queue length ...This paper analyzes a queue mode] of the polling system with limited service (K=1) in discrete time. By the imbedded Markov chain theory and the probability generating function method, the mean values of queue length and message waiting time are explicitly obtained. Also, we give the simulation results. The results obtained by H. Tagai (1985) are revised.展开更多
This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of ...This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.展开更多
研究了对电压源变流器型高压直流输电系统(voltage source converter-high voltage direct current,VSC-HVDC)的电压和电流的限幅控制。通过建立VSC-HVDC的离散化状态方程,分析电压、电流的稳态限幅控制和电流的动态限幅控制的关系,设...研究了对电压源变流器型高压直流输电系统(voltage source converter-high voltage direct current,VSC-HVDC)的电压和电流的限幅控制。通过建立VSC-HVDC的离散化状态方程,分析电压、电流的稳态限幅控制和电流的动态限幅控制的关系,设计了电流可工作范围的预测方法。建立了VSC-HVDC的串级控制系统,用外环控制功率目标,内环控制电流,在两环间加入动态限幅环节。对VSC-HVDC系统的启动状态和接收电网发生接地故障进行仿真,仿真显示动态电流限幅措施可以大大减小系统的波动和恢复时间,说明动态电流限幅对提高控制系统动态响应速度有明显效果。展开更多
The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e....The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.展开更多
基金the National Natural Science Foundation of China (Grant Nos.60232010 and 60572094)the National Natural Science Founda-tion of China for Distinguished Young Scholars (Grant No.60625104)
文摘As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform （including 3 main types： linear combination-type; sampling-type; and eigen decomposition-type）, and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 60504024） the Research Project of Zhejiang Provincial Education Department （Grant No. 20050905）.
文摘A novel neural network model, termed the discrete-time delayed standard neural network model （DDSNNM）, and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks （RNNs） and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed （or non-delayed） nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks （CNNs） and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.
文摘This paper analyzes a queue mode] of the polling system with limited service (K=1) in discrete time. By the imbedded Markov chain theory and the probability generating function method, the mean values of queue length and message waiting time are explicitly obtained. Also, we give the simulation results. The results obtained by H. Tagai (1985) are revised.
基金supported by the National Natural Science Foundation of China under Grant Nos.71171138,71301111,71571127the Scientific Research Innovation&Application Foundation of Headmaster of Hexi University under Grant Nos.XZ2013-06,XZ2013-09
文摘This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.
文摘研究了对电压源变流器型高压直流输电系统(voltage source converter-high voltage direct current,VSC-HVDC)的电压和电流的限幅控制。通过建立VSC-HVDC的离散化状态方程,分析电压、电流的稳态限幅控制和电流的动态限幅控制的关系,设计了电流可工作范围的预测方法。建立了VSC-HVDC的串级控制系统,用外环控制功率目标,内环控制电流,在两环间加入动态限幅环节。对VSC-HVDC系统的启动状态和接收电网发生接地故障进行仿真,仿真显示动态电流限幅措施可以大大减小系统的波动和恢复时间,说明动态电流限幅对提高控制系统动态响应速度有明显效果。
基金Postdoctoral Science Foundation of China (No. 20060400980)Postdoctoral Science Foundation of Shandong Province(No. 200603015)National Science Foundation of China (No. 10671112)
文摘The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.
