External Descriptions and Staircase Forms in Implicit Systems

Abstract

This paper studies the relationship between staircase forms and normal external descriptions in implicit systems. The authors show how to compute the proper and nonproper controllability indices of an implicit system using the reachability Hessenberg form and the corresponding normal external description. The normal external description of the system is computed using embedding techniques. Finally, the differences and similarities between the normal external descriptions computed are shown using the reachability and controllability Hessenberg forms of an implicit system.