二维周期系的指数型一致渐进稳定

On exponentially asymptotical stability of two dimensional linear differential with periodic coefficient

研究变系数二维周期系xy′=a(t)c(t)b(t)d(t)xy的结构稳定性.得出结论:只要周期函数a(t),c(t),b(t),d(t)的平均值之间满足一定条件,则可判定该方程正向(或负向)指数型渐近稳定,并应用实例来验证该定理.

Discussed exponentially asymptotical stability of periodic differential equation x y~′=a(t)c(t) b(t)d(t)x y, and obtained two new criteria on stability. The criteria can be directly arrived at from the relations between a(t), b(t), c(t) and d(t). In the end, cited an example to test the practicality on the criteria.