ABSTRACT

This paper deals with the problem of $H_{\mathrm{\infty }}$ control for linear descriptor systems with time-variable delay. The delay function, which is non-differentiable, appears in both the state and observation. For stability, appropriate Lyapunov–Krasovskii functionals are constructed to eliminate the derivative calculating of the delay function and utilize smaller number of linear matrix inequality decision variables. The proposed functionals are employed to derive new delay-dependent sufficient conditions for admissibility of the unforced descriptor closed-loop system. For $H_{\mathrm{\infty }}$ control, we design state feedback controllers which make the descriptor closed-loop system admissible with a maximum $H_{\mathrm{\infty }}$ disturbance attenuation level. A numerical example with simulation is given to illustrate the effectiveness of the proposed method.

摘要

本文针对以下问题 $H_{\mathrm{\infty }}$具有时变延迟的线性描述符系统的控制。不可微的延迟函数出现在状态和观察中。为了稳定性，构建了适当的 Lyapunov-Krasovskii 泛函以消除延迟函数的导数计算并利用较少数量的线性矩阵不等式决策变量。所提出的函数用于为非强制描述符闭环系统的可接受性推导出新的依赖于延迟的充分条件。为了$H_{\mathrm{\infty }}$ 控制，我们设计状态反馈控制器，使描述符闭环系统在最大 $H_{\mathrm{\infty }}$干扰衰减水平。给出了一个带有仿真的数值例子来说明所提出方法的有效性。