This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ₂‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.

中文翻译：

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基于差分代数表示的离散非线性系统的增益调度控制设计

本文讨论了用差分代数表示法（DAR）描述的非线性系统的局部稳定问题。开发了一组新的足够的线性矩阵不等式（LMI）条件，以设计增益预定状态反馈控制器。所提出的方法使用了依赖于参数的Lyapunov函数和新的辅助决策变量，旨在获得较少的保守结果。两个优化问题，提出要么获得最大的估计域的的引力（DOA）或最小化ℓ ₂从能量受限的干扰输入到性能输出。此外，本研究考虑了控制输入饱和和系统状态受多面体区域约束。提供了数值示例来说明所提出方法的有效性，并与最近发布的类似方法进行了有利的比较。