点时滞系统的反馈镇定

FEEDBACK STABILIZATION OF LINEAR SYSTEMS WITH POINT DELAYS IN STATE AND CONTROL VARIABLES

求解特征矩阵是镇定时滞系统的关键问题，本文给出了系统的特征根的代数重复度与几何重复度均为一般值的情况下特征矩阵的求法，即把它归结为求解一组线性代数方程的问题，并得到了该方程组有解及对应于同一特征值的解向量组线性独立的充分条件．本文还提出了一种算法来处理系统对应于不同特征值的左特征向量线性相关情况下系统的镇定问题．最后，举例说明了设计步骤．

Solving characteristics matrix equations (CME) of linear retarded systems isthe key problem for stabilizing the system using reduction technique.This paper gives thesolution of CME under the general condition that the eigenvalues occur in the spectrumof the system with algebraic and geometric multiplicities being greater than or equal toone.The main idea is to transform the CME into a group of linear algebraic equations(LAE).The sufficient conditions for the ekistence of the solution of the LAE and for theindependence of the solution vectors of the LAE corresponding to a given eigenvalue areestablished. An algorithm for dealing with the stabilization problem in the case that theleft eigenvectors of the system corresponding to different eigenvalues are linearly dependentis presented.An illustrative example is given to show the design procedure.