带有多个时滞的滞后型系统不稳定的充分条件

Sufficient Conditions for the Instability of Retarded Type Systems with Multiple Delays

研究了带有多个时滞的滞后型系统不稳定的充分条件.主要方法是基于系统的Lyapunov矩阵构造Lyapunov-Krasovskii泛函,然后在系统指数稳定的前提下,给出泛函的容许下界.它的否定就是系统不稳定的判据.最后数值例子验证了所得结果的有效性.

In this paper,we study the sufficient conditions for the instability of retarded type systems with multiple delays.The main method is to construct the Lyapunov-Krasovskii functional based on the Lyapunov matrix of the system.Furthermore,the allowable lower bound of the functional is given under the exponential stability of the system.Its negation is the criterion of system instability.Finally,the numerical example verifies the obtained result effectiveness.