滞后的迭代系统的结构与无条件关联稳定性(1)

随着计算机,特别是微型计算机的广泛应用,研究连续动力系统的离散化和工程实际中提出的任意滞后的迭代系统的结构与无条件关联稳定性是很有意义的课题。本文在1986年、1988年刘永清,李在根、叶乐年工作的基础上,采用1957～1960年秦元勋、刘永清创建的方法;给出了在传递滞后与采样周期成整数倍、分数倍与无理数倍时,任意滞后线性定常迭代系统的结构与无条件关联稳定性的充分与必要条件。并把此问题的超越方程求根的问题。化归为代数方程求根问题,还给出了n=1时具体运算过程与结果。对其它非定常、非线性等问题将另文论及。

THE STRUCTURE AND UNCONDITIONAL CONNECTIVE STABILITY OF ITERATIVE SYSTEMS WITH ANY TIME DELAY(1)

As successful applications of the computer,especially of themicro-computer in the control field,it is obviously meaningfulto Study both theoretical and practical problems arising fromdiscretization of a continuous time systems with any time delay,such as the structure concept and unconditional connectivestabitity.Based on the research results of Liu,Li and Ye(1986,1988),and using the method proposed by Chien and Liu duringthe period of 1957-1960,both the structure concept and thenecessary and sufficient conditions of the unconditional connec-tive stability of a linear,time-invariant,interative system withany time delay are given in this paper,for those cases of aninteger,fractional and irrational ratio of the sampling period tothe plant dead time.Moreover,a criterion on the roots of thetranscendental equation is now turned to a algebraic problem.Asan example,the concrete procedure and its results for the casen=1 are also shown as well.In addition,problems such as nonlin-earity and time-varying coefficient will be further discussed inour other papers.