This article is concerned with the guaranteed cost control problem for a class of fractional-order (FO) uncertain delayed linear systems with norm-bounded time-varying parametric uncertainty. Based on whether the states are available or not, guaranteed-cost state-based feedback stabilization and guaranteed-cost observer-based feedback stabilization for such system are addressed, respectively. By employing the linear matrix inequality (LMI) approach and FO Razumikhin theorem, two delay-independent guaranteed cost controller design methods and their guaranteed costs are first formulated, respectively, in which sufficient conditions of the state feedback and observer gains are presented in form of LMI. Two numerical examples are presented to demonstrate the effectiveness of the theoretical formulation.

中文翻译：

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时变时滞分数阶线性不确定系统的保证成本控制

本文关注一类具有范数有界时变参数不确定性的分数阶 (FO) 不确定延迟线性系统的保证成本控制问题。基于状态是否可用，分别解决了这种系统的基于保证成本状态的反馈稳定和基于保证成本观测器的反馈稳定问题。利用线性矩阵不等式（LMI）方法和 FO Razumikhin 定理，首先分别制定了两种与时延无关的保证成本控制器设计方法及其保证成本，其中状态反馈和观测器增益的充分条件以LMI。给出了两个数值例子来证明理论公式的有效性。