Circulation Design for Eigenvalue Replacement: Minimizing Gain Magnitude
针对可镇定线性系统，提出一种基于参数化特征结构配置的循环设计方法，在替换一阶实开环特征值时全局最小化增益幅度等指标，算法简单高效且无需矩阵求逆。
Based on a complete parametric partial eigenstructure assignment (ESA) approach, a circulation design for ESA in a stabilizable linear system via state feedback is proposed. It is shown that, in those rounds where a real open-loop eigenvalue of order 1 is replaced, a type of very general indices can be globally minimized, which include those for general eigenvector configuration and gain magnitude minimization as special cases. When all the open-loop eigenvalues to be replaced are real and are of order 1, the proposed circulation design turns out to be extremely simple and efficient, and also possesses good numerical reliability since the globally optimal solution is established in a simple, direct, and explicit form, and the proposed circulation algorithms remove completely matrix inverse operations. An illustrative example demonstrates the simplicity and effect of the proposed approach.