连续分布时滞抛物型系统的全局指数稳定性

Global exponential stability for parabolic systemswith continuous distributed delays

基于比较原理,利用推广的向量Hanalay微分不等式、Dini导数,结合Green公式及不等式分析技术,研究几类连续分布时滞的抛物型控制系统所导出的滑动模运动方程的全局指数稳定性问题。在仅要求系统的系数矩阵是个M 矩阵的条件下,证明了所获得的滑动模运动方程是全局指数稳定性的,建立了滑动模运动方程全局指数稳定性定理。并为研究连续分布时滞的抛物型系统的变结构控制问题奠定了基础。

Based on comparison principle, the global exponential stability for a class of sliding-mode equations rising in parabolic control systems with continuous distributed delays is investigated by using generalized vector Hanalay's differential inequality, Dini's derivative, Green's formula and technique of inequality analysis. On the condition that the coefficient of the systems is only an M-matrix, the obtained sliding-mode equations with continuous distributed delay are globally exponentially stable, and several theorems of the global exponential stability for the sliding-mode equations are established. The results on the global exponential stability of the parabolic systems with continuous distributed delays provide the theoretical foundation for variable structure control problem of the parabolic systems.