Minimal realization
In control theory, given any transfer function, any state-space model that is both controllable and observable and has the same input-output behaviour as the transfer function is said to be a minimal realization of the transfer function.<ref>Template:Citation.</ref><ref name="tan">Template:Citation.</ref> The realization is called "minimal" because it describes the system with the minimum number of states.<ref name="tan"/>
The minimum number of state variables required to describe a system equals the order of the differential equation;<ref>Template:Harvtxt, p. 91.</ref> more state variables than the minimum can be defined. For example, a second order system can be defined by two or more state variables, with two being the minimal realization.
Gilbert's realizationEdit
Given a matrix transfer function, it is possible to directly construct a minimal state-space realization by using Gilbert's method (also known as Gilbert's realization).<ref>Template:Cite book</ref>