Structural properties and poles assignability of LTI singular systems under output feedback

This paper studies the structural properties of both 3nite poles and the in3nite pole of linear time-invariant singular systems under output feedback. Three main problems are studied, namely, (1) the algebraic structures of both 3nite poles and the in3nite pole; (2) the assignability of 3nite poles and the elimination of the in3nite pole by output feedback; and (3) the controllability and observability of the system with minimal number of inputs and outputs. New generic solutions to these problems are presented in terms of some new concepts de3ned in this paper including the geometric multiplicity of the in3nite pole, the 3nite and impulsive output feedback cycle indices of the system. Determination of these multiplicities and indices are discussed. An assignability equivalence is established between the variable 3nite poles and the poles of a controllable and observable non-singular system. The number of the independent in3nite poles that can be reduced is given in terms of the system matrices. The minimal number of inputs and outputs that guarantee controllability and observability are shown to be the output feedback cycle indices. ? 2003 Elsevier Science Ltd. All rights reserved.