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Lyapunov–Krasovskii functionals for input-to-state stability of switched non-linear systems with time-varying input delay

机译：Lyapunov–Krasovskii函数用于改变时滞的输入非线性系统的输入状态稳定性

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摘要

This study investigates the input-to-state stability issue and the Lyapunov–Krasovskii functional construction for a class of switched non-linear systems with time-varying input delay under mode-dependent average dwell-time scheme. The authors assume that an exponential stabilising state feedback controller has been predesigned for the nominal system and the Lyapunov function for the nominal closed-loop system is available. When input delay and disturbance are involved, the closed-loop system may be unstable under the average dwell time for the nominal system. In allusion to this instance, by introducing a positive definite relaxation matrix and constructing a novel piecewise Lyapunov–Krasovskii functional based on the known Lyapunov function, they provide sufficient conditions and the upper bound of the input delay such that the closed-loop system is input-to-state stable with respect to the disturbance. Finally, numerical examples are given to illustrate the effective of the proposed method.
机译：这项研究调查了在依赖于模式的平均停留时间方案下，一类时变输入时滞的切换非线性系统的输入状态稳定性问题和Lyapunov–Krasovskii函数构造。作者假设为标称系统预先设计了指数稳定状态反馈控制器，并且标称闭环系统的Lyapunov函数可用。当涉及输入延迟和干扰时，闭环系统在标称系统的平均停留时间下可能会不稳定。在这种情况下，通过引入正定松弛矩阵并基于已知的Lyapunov函数构造新颖的分段Lyapunov–Krasovskii函数，它们提供了充足的条件和输入延迟的上限，从而可以输入闭环系统状态相对于干扰是稳定的。最后，通过数值算例说明了该方法的有效性。

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