LAUSR

In this paper, based on the inverse of block companion matrix pencils associated with matrix polynomials, a first-order state-space realization in descriptor system form for a general high-order linear system is derived. An important feature of the proposed realization is that it allows the high-order linear system to be singular. While in the case that the high-order system is nonsingular, two realizations in normal state-space system forms are directly deduced. With the help of the proposed realization, a generalized Popov Belevitch Hautus (PBH) criterion for high-order systems is then established in terms of the original system matrix polynomials. Examples are studied which well demonstrate the proposed theories.