Asymptotic stability of a class of linear discrete systems with multiple independent variables

被引:0
作者
Liu, DR [1 ]
Molchanov, A [1 ]
机构
[1] Univ Illinois, Dept Elect & Comp Engn, Chicago, IL 60607 USA
关键词
discrete shift-invariant systems; shift-varying systems; asymptotic stability; robust stability; Lyapunov methods;
D O I
暂无
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
This paper investigates the problem of asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. We establish the equivalence of this problem and that of robust stability for a class of ordinary linear shift-varying discrete systems with the matrix uncertainty set defined by the coefficient matrices of the original system. On the basis of this equivalence, by using the variational method and Lyapunov's second method, necessary and sufficient conditions for asymptotic stability are obtained in different forms for the class of systems considered. The parametric classes of Lyapunov functions which define the necessary and sufficient conditions of asymptotic stability are determined. We use the piecewise linear polyhedral Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for asymptotic stability of the given class of discrete systems in the form of solvability conditions of a set of matrix equations. A simple sufficient condition of asymptotic stability is also obtained which becomes necessary and sufficient for several special cases of the discrete systems under consideration.
引用
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页码:307 / 324
页数:18
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