Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System

Zhang Jiye

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Zhang Jiye. Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System[J]. Applied Mathematics and Mechanics, 1995, 16(10): 927-932.

Citation:

Zhang Jiye. Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System[J]. Applied Mathematics and Mechanics, 1995, 16(10): 927-932.

Citation:

Zhang Jiye. Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System[J]. Applied Mathematics and Mechanics, 1995, 16(10): 927-932.

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Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System

Zhang Jiye

Research institute of Applied Mechanics, Southwest Jiaotong Universtity, Chengdu 610031, P. R. China

Received Date: 1994-10-05
Publish Date: 1995-10-15

Abstract

Abstract

In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control system in which the nonlinear function f(σ) satisfying conditions follows f(0)=0,σf(σ)>0(σ≠0)(2) or f(0)=0,0≤k₁≤f(σ)/σ≤k₂<+∞(σ≠0)(3) It gives the necessary and sufficient conditions for the absolute stability for system(1) under conditions(2).We also obtain the sufficient for absolute stability of the simplified system of(1) under conditions(3).
- discrete type,
- absolute stability,
- necessary and sufficientcondition,
- Lune problem

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References(14)

References

[1]	A,M.Letov,Stability of Nonl inear Con trot S ystems门955)(in R ussian);English transl.of 1st.ed.,Princeton University Press,Princeton(1961).
[2]	舒仲周,稼运动稳定性》,西南交通大学出版社,成都(1989).
[3]	廖晓听.《稳定性的数学理论与应用争,华中师范大学出版社,武汉(1988).
[4]	秦元勋等,《运动稳定性理论与应用》,科学出版社,北京(1981).
[5]	朱思铭,直接控制系统的绝对稳定性准则,中山大学学报,(3)(1979),20-28.
[6]	谢惠民,一类三阶控制系统绝对稳定性的充分必要条件.中国科学(A),(9)(1981),1165-1175.
[7]	张继业、舒仲周,直接控制系统绝对稳定的充要性准则,应用数学和力学,15(3)(1994),245-251.
[8]	裘晓钢、舒仲周,控制系统第二标准型的绝对稳定性准则,应用数学和力学,7(9)(1988),785-800.
[9]	廖晓听,论离散型Луръе控制系统绝对稳定的充要条件,数学年刊,10(A)(5)(1989),628-635.
[10]	Lj.T.Grujic and D,D,Siljak,E gponential stability of large-scale direct systems,Int,J.Control.,19(3)(1974),481-491.
[11]	肖淑贤,离散型月Луръе控制系统的降维原理和应用,华中理工大学学报,20(增刊)(1992),97-101.
[12]	Chen Chitsong,Linear System Theory,and Design,2nd,Holt,Rinehart and Winston,New York(1984).
[13]	J,P.La Salle,The Stability of Dynamical Systems,SIAM,Philadelphia(1976).
[14]	李森林,几类直接控制系统绝对稳定的充分及必要条件,应用数学学报,6(4)(1983),458-467.