利用GRONWAL定理确定非线性电路平衡点全局渐近稳定性

Study on the Global Aymptotic Stability of the Equilibrium Point of Nonlinear Circuits by Gronwall Lemma

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。这种方法以GRONWALL定理为基础 ,结合平衡点的渐进稳定判断依据 ,决定平衡点的全局渐近稳定性。与目前所采用的LIYAPUNOV直接法相比 ,该法具有无须判断平衡点的唯一性 ,判别方程直接明了等优点。同时 ,该法对于其他形式的非线性系统的分析 。

In this paper,based on Gronwall lemma,a new method to analyze the global asymptotic stability of the equilibrium point of nonlinear circuit is advanced.The conditions for the global asymptotic stability of the equilibrium point are expressed as the inequalities of the some matrixes norms and measures including the coefficient.By the method in this paper,to decide the global asymptotic stability of the equilibrium point ,it is not necessary to verify whether the equilibrium point is unique and to construct Liyapunov functions.And the requirements in the conditions for the circuit elements are only their slopes be bounded,which are much loose than those in previously published papers.so the work of this paper is an extension for the classical results already kmown.