Dynamical order assignment in linear descriptor systems via state derivative feedback

In this paper, the dynamical order assignment problem for linear descriptor systems via state derivative feedback is studied. A new, direct and simple parametric approach is presented, which assigns via state derivative feedback any desired allowable dynamical order of the closed-loop system. A simple, general direct and complete parametric expression for all the feedback gains which assign the desired dynamical order of the closed-loop system is established. Based on this result, a general complete parameterization of all those feedback gains possessing the minimum Frobenius norm is further presented. The proposed approach is convenient to use and possesses good numerical reliability since it mainly involves singular value decompositions and inverses of positive definite diagonal matrices. The presented example shows these advantages and the simplicity of the proposed approach.