Abstract
Based on the generalized definition of an equivalent system, two phase variable canonical forms are given for linear multi-inputs and multi-outputs systems, i.e., the canonical form for control and the canonical form for observation. It is shown that a characteristic quantity called the stage sequence can be defined for each given system to uniquely determine the structure of its canonical form. Having very compact structures, these canonical forms give excellent representations of the physical and mathematical composition of systems and are particularly convenient for analyses of optimal control problems.
