用Bohl-Perron型定理证明线性差分方程的新稳定性条件
New Stability Conditions for Linear Difference Equations using Bohl-Perron Type Theorems
摘要：
Bohl-Perron关于线性差分方程$$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$的指数二分性的结果表明（在某些自然条件下），如果非齐次方程的所有解都有界，则相应的齐次方程是指数稳定的.根据它的推论，如果一个给定的方程{ \em close}到一个指数稳定的比较方程（某个算子的范数小于1），则所考虑的方程是指数稳定的.对于具有多个变时滞和系数的差分方程，利用上述结果，解的表示和具有正基本函数的比较方程，得到了新的指数稳定性检验.
英文摘要：
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is {\em close} to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.
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