Observable state space realizations for multivariable systems

This paper derives two canonical state space forms (i.e., the observer canonical form and the observability canonical form) from multiple-input multiple-output systems described by difference equations. The state space model is expressed by the first-order difference equation and is equivalent to the input–output representation. More specifically, by setting the different state variables, the difference equations or the input–output representations can be transformed into two observable canonical forms and the canonical state space model can be also transformed into the difference equations. Finally, two examples are given.