Canonical Forms of Linear Multivariable Systems

This paper considers the problem of finding a complete set of invariants and canonical forms for a linear, time-invariant, multivariable system $(A,B,C)$ under a group of transformations. The group consists of input coordinate transformations, state coordinate transformations and state feedback transformations. A set of canonical forms is derived. A set of invariants called the transmission zeros is given, which has application to the servomechanism problem.