利用广义李雅普·诺夫方法，研究了广义非线性离散系统，给出了广义非线性离散系统稳定性定理和不稳定性定理。
The method of singular Lyapunov's function is employed to study the singular nonlinear discrete systems, the theorem of stability and the theorem of no stability on it are given.
结果表明：该分析定理与线性系统的李雅普诺夫稳定性定理是一致的。
The results show that the stability analysis theorem is consistent with the Liapunov stability theorem for linear systems.
利用李雅普诺夫渐近稳定性定理，很方便地实现了洛沦滋和类洛沦滋系统的混沌自同步。
Using the theory of Lyapunov asymptotic stability, the chaos self synchronization of Lorenz system and analogy Lorenz system are easily realized.
事实上，基于李雅普·诺夫函数的稳定理论，也可从耗散性的角度加以分析。
In fact, Lyapunov stable theorems can also be expressed by dissipative theory.
进而，利用李雅普·诺夫函数和比较定理确定了持续生存的条件。
Conditions for permanence is established via the method of comparison involving multiple Liapunov functions.
通过使用辅助系统方法，我们给出了基于李雅普·诺夫稳定性理论的广义同步定理。最后，用数值例子来验证定理的有效性。
By using the auxiliary system method, a sufficient condition for GS is derived based on the Lyapunov stability theory. At last, numerical examples are presented which fit the theoretical analysis.
通过使用辅助系统方法，我们给出了基于李雅普·诺夫稳定性理论的广义同步定理。最后，用数值例子来验证定理的有效性。
By using the auxiliary system method, a sufficient condition for GS is derived based on the Lyapunov stability theory. At last, numerical examples are presented which fit the theoretical analysis.
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