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A Razumikhin approach to exponential admissibility of switched descriptor delayed systems

机译：Razumikhin方法解决切换描述符时滞系统的指数容许性

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This paper addresses on the robust exponential admissibility of uncertain switched descriptor systems with time-varying delays. Firstly, an easily verified condition is presented to check the switching-impulsive-free which ensures the consistent of algebraic equations. Moreover, a novel type of piecewise Lyapunov functions which are decreasing at switching times is introduced. This type of delicately constructed Lyapunov functions can efficiently eliminate the switching jump of adjacent Lyapunov functions at switching instants. By this type of Lyapunov functions and Razumikhin-type technique, the delay-independent minimum dwell time criteria of robust exponential admissibility are established under switching-impulsive-free. Two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.
机译：本文讨论了具有时变时滞的不确定切换描述符系统的鲁棒指数容许性。首先，提出了一个容易验证的条件来检查无开关冲动，这确保了代数方程的一致性。此外，介绍了一种新型的分段Lyapunov函数，这些函数在切换时间逐渐减少。这种精心构造的Lyapunov功能可以在切换瞬间有效消除相邻Lyapunov功能的切换跳跃。通过这种Lyapunov函数和Razumikhin型技术，建立了无开关无脉冲条件下鲁棒指数可容许性的与延迟无关的最小停留时间准则。给出两个说明性的数值示例，以显示所获得的理论结果的有效性。

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