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本文提出了一种新的分析非线性电路平衡点全局渐近稳定的方法。这种方法利用冻结系数的相关概念,结合平衡点的渐近稳定判据从而决定平衡点的全局渐近稳定性。与目前该问题所采用的LIYAPUNOV直接法相比,该方法具有无须判断非线性系统平衡点的唯一性和构造LYAPUNOV函数的优点。同时,该方法对于其它形式的非线性系统的分析,也有重要的启发性及应用价值。
In this paper, a new method to analyze the global asymptotic stability of the equilibrium point of nonlinear circuits is proposed. This method makes use of the related concepts of the freezing coefficient and the asymptotic stability criterion of the equilibrium point to determine the global asymptotic stability of the equilibrium point. Compared with the LIYAPUNOV direct method adopted by the current problem, the method has the advantages of not needing to judge the uniqueness of the equilibrium point of the nonlinear system and constructing the LYAPUNOV function. At the same time, this method also has important enlightenment and application value for the analysis of other forms of nonlinear systems.