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中文摘要：
用Lyapunov方法研究非线性时变离散系统的渐近稳定性．如果存在与时间无关的止定Lyapunov函数，它沿着系统的轨道不增，同时附加类似于Barbashin—Krasovskii定理中描述的一个条件时，即可得到渐近稳定的结论．将此结果分别应用到自治系统和周期系统时，即可得离散情况下的LaSalle定理和Barbashin—Krasovskii定理．
英文摘要：
The asymptotic stability of nonlinear time-varying discrete-time systems was studied by using Lyapunov approach. If there exists time independent Lyapunov function V that is positively definite, and its difference is non-increased along the solutions of the systems, plus the additional condition imposed as the one of statements of the Barbashin-Krasovskii theorem, the conclusion of asymptotic stability will be obtained. In applications of Theorem 1 to the time-invariant and periodic systems respectively, the LaSalle theorem and Barbashin-Krasovskii theorem can be reobtained.
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