Exponential Stability of Linear Systems with Multiple Time-varying Delays

为一般延迟的动态系统和二个初步的词根基于确定的新型的指数的稳定性定理，为有多重变化时间的延期的线性系统的不太保守的稳定性条件被使用 Lyapunov 的新稳定性分析途径建立函数。不同于在文学的一些结果，任何一个都不确定的结果取决于变化时间的延期的衍生物。因此，结果对有很快的变化时间的延期的盒子合适。一个例子被提供证明获得的稳定性条件比在文学基于标准 Razumikhin 类型条件直接获得的好。

Based on the established new-type exponential stability theorem for general retarded dynamical systems and two preliminary lemmas, less conservative stability conditions for linear systems with multiple time-varying delays are established by using the new stability analysis approach of Lyapunov function. Unlike some results in the literature, none of the established results depends on the derivatives of the time-varying delays. Therefore, the results are suitable to the cases with very fast time-varying delays. An example is provided to show that the stability conditions obtained are better than the ones obtained directly based on the standard Razumikhin-type condition in the literature.