离散型线性定常系统的摄动矩阵李亚普诺夫方程的若干问题
Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems
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摘要: 本文讨论了离散型线性定常系统在系统参数发生扰动时的李亚普诺夫稳定性与波波夫超稳定性.给出了容许的摄动界,使得离散型线性系统的李亚普诺夫稳定性与波波夫超稳定性的维持得到了保证.该结果在MRAC(模型参考自适应控制)中是具有意义的.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.
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[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). -
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