A Direct Method for Possible Nilpotent Jordan Matrices of State Deadbeat Controllers

Abstract

This paper discusses a direct method for possible nilpotent Jordan matrices of state deadbeat controllers. The relation between the indices which are defined to obtain a nilpotent Jordan matrix and the degrees of the blocks of a nilpotent Jordan matrix is explained through a figure. By using this figure, a simple equation which shows the relation between the controllability indices of the system and the degrees of the blocks is derived. Then, all possible nilpotent Jordan matrices which are similar to the system matrix of the feedback system controlled by a state deadbeat controller can be directly obtained only from the controllability indices of the system.