Realization algorithm for constructing a controllable representation of a singular system with a special coordinate

Abstract

A realization algorithm that constructively determines a controllable representation of a singular system from a so-called column-pseudoproper right MFD defined by Tan and Vandewalle in 1987 is proposed. Not only is the realized system proved to be controllable in the sense of Cobb but also a special coordinate form can be simultaneously achieved, which has been widely used in singular system design and analysis in recent years. By the formulation presented in this paper, the conditions for the realized system to be observable, which are insufficiently discussed by Tan and Vandewalle, are readily derived. It appears that our structure may be more easily employed to check whether the realized system satisfies the observability conditions or not than theirs