变时滞分布参数系统的全局指数稳定性

Global exponential stability for distributed parameter systems with varying time-delay

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,研究几类变时滞分布参数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,在仅要求系数矩阵是个M-矩阵的条件下,获得了几类滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理.推广和改进了前人的结论.并为研究时滞分布参数系统的变结构控制问题奠定了基础.

Based on the comparison principle,the global exponential stability for a class of sliding mode equations rising in distributed parameter control system with varying time-delay is investigated by using general vector Hanalay＇ s differential inequality,Dini＇ s derivative, Green formulation, and technique of inequality analysis. Under the conditions that the coefficient of distributed parameter system is an M-matrix, sufficient conditions are derived for global exponential stability for the sliding mode equations with varying time-delay and several theorems of the global exponential stability for the sliding mode equations are established. It is shown that the estimates obtained from the Hanalay-type inequalities improve the estimates obtained from Lyapunov methods. Some previous works are improved. The results on the global exponential stability of the distributed parameter control systems with varying time-delay provide the theoretical foundation for the variable structure control problem of the distributed parameter systems.