Normal forms of linear multivariable square systems and their application

Abstract

Normal forms called by Byrnes-Isidori are useful to study properties of zeros of systems in continuous-time and sampled-data domain for the design of feedback controllers. This paper investigates how transfer function matrices and state-space equations of linear square systems with controllability, observability and invertibility are transformed to normal forms. In addition, as an application of a normal form, an approximate expression of zeros of a sampled-data model corresponding to a continuous-time square system nondecouplable by static state feedback is derived for a small sampling period.