A new methodology to design an $${H}_{\infty }$$ H ∞ observer-based controller for discrete-time delayed systems subject to input saturation and $${\mathcal {L}}_{2}$$ L 2 -norm disturbances is proposed, motivated by a benchmark problem. The stabilizing observer-based controller gains are obtained from an LMI formulation using a Lyapunov–Krasovskii functional, free weighting matrices, and an effective approach to overcome the obstacle of the bilinearity. To select the most adequate controller, an iterative optimization algorithm is developed to maximize the set of admissible initial conditions. The proposed results are illustrated by a practical application using the quadruple tank process to visualize different control theory notions and phenomena in laboratory conditions.

中文翻译：

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受输入饱和和干扰影响的延迟系统的新型基于观测器的控制器设计

一种设计 $${H}_{\infty }$$ H ∞ 基于观测器的控制器的新方法，适用于受输入饱和和 $${\mathcal {L}}_{2}$$ 影响的离散时间延迟系统L 2 -范数扰动被提出，由基准问题驱动。使用 Lyapunov-Krasovskii 泛函、自由加权矩阵和克服双线性障碍的有效方法，从 LMI 公式中获得稳定的基于观测器的控制器增益。为了选择最合适的控制器，开发了一种迭代优化算法来最大化允许的初始条件集。所提出的结果通过实际应用加以说明，该实际应用使用四缸过程在实验室条件下可视化不同的控制理论概念和现象。