Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems

Huang Lin; Zhu Wei-ling

Volume 4 Issue 1

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(1): 93-101

Huang Lin, Zhu Wei-ling. Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems[J]. Applied Mathematics and Mechanics, 1983, 4(1): 93-101.

Citation:

Huang Lin, Zhu Wei-ling. Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems[J]. Applied Mathematics and Mechanics, 1983, 4(1): 93-101.

Citation:

Huang Lin, Zhu Wei-ling. Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems[J]. Applied Mathematics and Mechanics, 1983, 4(1): 93-101.

PDF( 550 KB)

Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems

Mechanics Department, Beijing University, Beijing

Received Date: 1982-01-21
Publish Date: 1983-02-15

Abstract

Abstract

Both the Lyapvnov stability and Popov's hypex-stability of discrete linear time-invariant system in case of system parameter disturbance are discussed in this paper. The allowable disturbance ranges are given so that the maintenance of the Lyapunov stability and the Popov's hyperstability of a discrete linear system is guaranteed. The results find their significance in the MRAC.

FullText(HTML)

References(8)

References

[1]	黄琳,《系统与控制理论中的线性代数》,即将出版,科学出版社,北京.
[2]	Narendra,K.S.,Adaptive Control——MRAC,Lecture Notes of the Lecture Delivered in Nanjing Institute of Technology,Sept.(1981).
[3]	Narendra,K.S.and L.S.Valavani,A comparison of Lyapunov and hyperstability approaches of adaptive control of continuous systems,IEEE Trans.on Ac-25,(1980).
[4]	Anderson,B.D.O.,A simplified viewpoint of hyperstability,IEEE Trans.on AC-13,(1968).
[5]	Kalman,R.E.,Lyapunov function for the problem of Lure in automatic control,Proc.of the NAS of the U.S.A.,(1963).
[6]	Landau,Y.D.,Adaptive Control,Model Reference Approach.
[7]	黄琳,郑应平,李亚普诺夫第二方法与多变量线性系统,《控制理论会议文集》,厦门,科学出版社,北京,(1979).
[8]	Zhu Wei-ling(朱伟灵) and Hwang Ling(黄琳),Some problems concerning the hyperstability theory in design of adaptive control,Proceedings of the Biannual Meeting on Control Systems,Shanghai,(1981).

Relative Articles

[1]	TAN Shu-jun, ZHOU Wen-ya, WU Zhi-gang. An Extended Precise Integration Method for Solving Inhomogeneous Two-Point Boundary Value Problems of Linear Time-Invariant Systems[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1145-1157. doi: 10.3879/j.issn.1000-0887.2015.11.003
[2]	LIN Su-rong, MO Jia-qi. Nonlinear Singularly Perturbed Problems of Ultra Parabolic Equations[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1249-1253.
[3]	LUO Zhen-dong, MAO Yun-kui, ZHU Jiang. Nonlinear Galerkin Mixed Element Methods for the Stationary Incompressible Magnetohydrodynamics[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1486-1496.
[4]	Krishna Kumar, B. K. Sharma. Bruck Formula for a Perturbed Lipschitzian Iteration of Lipschitz Pseudocontractive Maps[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1293-1300.
[5]	LIU Bao-guo, YIN Xue-gang, JIAN Kai-lin, WU Yong. Perturbation Transfer Matrix Method for Eigendata of One-Dimensional Structural System With Parameter Uncertainties[J]. Applied Mathematics and Mechanics, 2003, 24(7): 708-714.
[6]	LUO Zhen-dong, ZHU Jiang. A Nonlinear Galerkin Mixed Element Method and a Posteriori Error Estimator for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1061-1072.
[7]	LUO Zhen-dong, ZHU Jiang, WANG Hui-jun. A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(7): 697-706.
[8]	HE Yin-nian, LI Kai-tai. Nonlinear Galerkin Method for the Exterior Nonstationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1141-1149.
[9]	ZHU Chuan-xi. Some Problems in the Z-C-X Space[J]. Applied Mathematics and Mechanics, 2002, 23(8): 837-842.
[10]	Mei Liquan. A Spectral Streamline Diffusion Finite Element Coupled Method of Unsteady Transport Equation in the Field of Neutron Logging[J]. Applied Mathematics and Mechanics, 1999, 20(7): 691-698.
[11]	Liang Zai-zhong. A Study of the Construction of Lyapunov Function for a Class of Fourth Order Nonlinear Systems[J]. Applied Mathematics and Mechanics, 1995, 16(2): 181-188.
[12]	Su Yu-cheng, Shen Quan. The Numerical Solution of a Singularly Perturbed Problem for Quasilinear Parabolic Differential Equation[J]. Applied Mathematics and Mechanics, 1992, 13(6): 479-488.
[13]	Su Yu-cheng, Shen Quan. The Numerical Solution of a Singularly Perturbed Problem for Semilinear Parabolic Differential Eqnation[J]. Applied Mathematics and Mechanics, 1991, 12(11): 979-988.
[14]	Lü Zhen-hua, Feng Zhen-dong, Fang Chuan-liu. A New IVIatrix Perturbation Method for Analytical Solution of the Complex Modal Eigenvalue Problem of Viscously Damped Linear Vibration Systems[J]. Applied Mathematics and Mechanics, 1991, 12(8): 719-728.
[15]	Zhang Shu-shun, Shang Da-zhang. The Theorem of the Stability of Nonlinear Nonautonomous Systems under the Frequently-Acting Perturbation——Liapunov’s Indirect Method[J]. Applied Mathematics and Mechanics, 1991, 12(7): 671-678.
[16]	Cheng Xiang-sheng. On Some Problems in Dynamic Computation for Thin-Walled Structures[J]. Applied Mathematics and Mechanics, 1990, 11(7): 653-657.
[17]	Wu Chi-guang, Su Yu-cheng, Sun Zhi-zhong. Asymptotic Method for Singular Perturbation Problem of Ordinary Difference Equations[J]. Applied Mathematics and Mechanics, 1989, 10(3): 211-220.
[18]	Zhang Shu-shun. The Theorem of the Stability of Linear Nonautonomous ystems under the Frequently-Acting Perturbation[J]. Applied Mathematics and Mechanics, 1986, 7(2): 169-171.
[19]	Zhong Wan-xie, Li Xi-kui. On Some Problems in the Assembling of Multilevel Substructuring[J]. Applied Mathematics and Mechanics, 1982, 3(5): 577-584.
[20]	Hwang Ling, Zhu Wei-ling. The Small Disturbance Problems Associated with the Algebraic Riccati Equation of Continuous Linear Time-Invariant Systems[J]. Applied Mathematics and Mechanics, 1982, 3(5): 653-660.