Multi-stage design procedure for modal controllers ofmulti-input defective systems

The modal controller of single-input system cannot stabilize the defective system with positive real part of repeated eigenvalues, because some of the generalized modes are uncontrollable. In order to stabilize the uncontrollable modes with positive real part of eigenvalues, the multi-input system should be introduced. This paper presents a recursive procedure for designing the feedback controller of the multi-input system with defective repeated eigenvalues. For a nearly defective system, we first transform it into a defective one, and apply the same method to manage. The proposed methods are based on the modal coordinate equations, to avoid the tedious mathematic manipulation. As an application of the presented procedure, two numerical examples are given at end of the paper.