This paper considers the parametric control to the Lorenz system by state feedback. Based on the solutions of the generalized Sylvester matrix equation (GSE), the unified explicit parametric expression of the state feedback gain matrix is proposed. The closed loop of the Lorenz system can be transformed into an arbitrary constant matrix with the desired eigenstructure (eigenvalues and eigenvectors). The freedom provided by the parametric control can be fully used to find a controller to satisfy the robustness criteria. A numerical simulation is developed to illustrate the effectiveness of the proposed approach.

中文翻译：

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基于状态反馈的Lorenz系统鲁棒参数控制

本文考虑通过状态反馈对Lorenz系统进行参数控制。基于广义Sylvester矩阵方程（GSE）的解，提出了状态反馈增益矩阵的统一显式参数表达式。Lorenz系统的闭环可以转换为具有所需特征结构（特征值和特征向量）的任意常数矩阵。参数控制提供的自由度可以完全用于找到满足鲁棒性标准的控制器。数值模拟表明了该方法的有效性。