This paper deals with stabilisation, and static output feedback synthesis, under structure constraints for linear time-invariant systems. The proposed approach relies on a prominent property of Hurwitz-stable matrices set and a Douglas-Rachford (DR) reflection method type for finding a point in the intersection of two closed sets. The method proposed in this paper emulates the genericity of the Linear Matrix Inequalities framework while keeping the feedback gain separated from any matrix with direct or indirect connection to the Lyapunov function. The link between the sequence of iterates generated by the proposed algorithm and a continuous dynamical system results in the use of Lyapunov stability theory for guaranteeing the local convergence. Several examples are given to prove the validity of the proposed method.

中文翻译：

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用于合成具有保证局部收敛的结构化控制器的基于反射的技术

本文讨论了线性时不变系统在结构约束下的稳定性和静态输出反馈综合。所提出的方法依赖于 Hurwitz 稳定矩阵集的突出特性和 Douglas-Rachford (DR) 反射方法类型，用于在两个封闭集的交集中找到一个点。本文提出的方法模拟了线性矩阵不等式框架的通用性，同时将反馈增益与任何与李雅普诺夫函数直接或间接连接的矩阵分开。所提出的算法生成的迭代序列与连续动力系统之间的联系导致使用李雅普诺夫稳定性理论来保证局部收敛。给出了几个例子来证明所提出方法的有效性。