Abstract

In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

中文翻译：

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具有多个时变时滞的线性描述符系统的基于状态反馈观测器的控制设计

摘要

在本文中，我们提出了一种基于线性矩阵不等式（LMI）的设计方法，以解决基于观测器的具有多个时变时滞的线性描述符系统的控制问题。延迟函数可以是连续且有界的，但不一定是可微的。首先，通过引入一套新的改进的Lyapunov–Krasovskii函数，避免计算延迟函数的导数，我们获得了新的依赖于延迟的充分条件，以保证系统是规则的，无脉冲的且渐近稳定的。然后，基于导出的稳定性条件，我们通过LMI设计状态反馈控制器和观察者增益，这可以在标准计算算法中以数值方式求解。给出了一个带有仿真的数值例子，以证明所提出的设计的效率和有效性。