用优化比较方程的核判别大系统的稳定性

采用K类函数法从非线性大系统集结出损失最小（相对已取得的矢量Lyapunov函数而言）的比较方程（自治非线性的）,并从中取出相对简单的核方程。对后者以单调倾负曲线为脊柱构造了箱体Lyapunov函数,判定了大系统的渐近稳定性。所得判据是核方程已知量的代数显式,便于应用。

ASYMPTOTICAL STABILITY OF LARGE SCALE SYSTEMS VIA NUCLEUS OF OPTIMAL COMMRISON EQUATIONS

In this paper, an optimal comparison equation is aggregated from a nonlinear large scale system with the least loss relative to the known vector Lyapunov Functions. The right hand side of the comparison equation is the difference between two K-type functions. In those two functions we ferret out two new K-type functions to form a new difference simpler than the old. Using the new difference, we establish a new differential equation called the nucleus of the comparison equation. Then we prove that if a certain condition is fulfilled, the nucleus equation possesses a monotonically inclined negative curve whose parameter equations has monotonically increasing functions on their right hand side and each point on which has a negative "velocity". By means of a scalar box-Lyapunov function with a backbone yielded by the monotonically inclined negative curve of the nucleus equation, the asymptotical stability of the large scale systems is determined. The resultant criterion is convenient for applications because it is an algebraic explicit formula constituted by the known quantities of the nucleus equation.