This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

中文翻译：

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时滞非线性系统动态输出反馈控制设计新方法

本文介绍了一种用于以线性参数变化（LPV）系统为代表的时变延迟离散时间非线性系统的全阶动态输出反馈（DOF）控制器。控制器设计是通过使用 Lyapunov-Krasovskii 稳定性参数开发基于延迟的线性矩阵不等式的条件来进行的。该方法的一个显着特点是直接获得动态控制器增益，不需要变量变换、等式约束或迭代算法。这一功能使其有别于文献中的许多现有方法，并简化了设计过程。此外，所提出的方法保证了闭环系统原点的局部渐近稳定性，并提供了估计的允许初始条件区域。一旦在允许的初始条件区域内启动的状态轨迹保持在LPV模型的有效域内，就可以确保系统的正确运行。提供了数值示例来说明所提议条件的潜力和有效性。