Global exponential stability for distributed parameter systems with varying time-delay
变时滞分布参数系统的全局指数稳定性

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.