二阶Sylvester方程的解及其在特征结构配置中的应用

考虑了二阶Sylvester矩阵方程的求解及其在特征结构配置设计中的应用。通过矩阵初等变换,给出了该矩阵方程的迭代形式的解析通解。基于二阶Sylvester矩阵方程的解析通解,给出了振动二阶线性系统的状态反馈特征结构配置设计参数化方法。该参数化方法给出了特征向量矩阵和状态反馈增益阵的参数化表达式,其所含自由参数为控制系统设计提供了全部自由度,可适当选择这些参数满足某些系统设计性能指标,如鲁棒性等。最后,数值算例表明二阶Sylvester矩阵方程的解析通解和状态反馈特征结构配置设计参数化方法的简单有效性。

Solutions of Second-order Sylvester Matrix Equation and Its Application in Eigenstructure Assignment

Solutions of a class of second-order Sylvester matrix equation and its application in the design of eigenstructure assignment are investigated.By using some elementary matrix transformations,an analytical general solution of the second-order Sylvester matrix equation is obtained in an iterative form.Based on the proposed analytical general solution of the second-order Sylvester matrix equation,a parametric method of the state feedback eigenstructure assignment in a class of vibration second-order linear systems is presented.This parametric method offers the parametric expressions for all the eigenvector matrices and the state feedback gain matrices.And this method includes all the design degrees,which can be further selected to satisfy some performance index,such robustness.Finally,a numerical example shows the simplicity and effectiveness of the analytical general solution to the second-order Sylvester matrix equation and the parametric method of state feedback eigenstructure assignment.