Feedback Stabilization of Linear Systems with Distributed Delays in State and Control Variable
分布时滞系统的反馈镇定

Solving characteristic matrix equation (CME) of a linear retarded system is a key problem for stabilizing the system by use of reduction technique. This paper gives the solution of CME under the general condition that the eigenvalues occur in the spectrum of the system with algebraic and geometric multiplicities being greater than or equal to one. The main idea is to transform CME into a group of linear algebraic equations (LAE). The sufficient conditions for the existence of the solution of LAE and for the independence of the solution vectors of LAE corresponding to a given eigenvalue are established. When the left eigenvectors of the system corresponding to different eigenvalues are linearly dependent, all algorithm for dealing with the stabilization problem is presented.