control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

, given any transfer function, any state-space model that is both

controllable Controllability is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observabi ...

and observable and has the same input-output behaviour as the transfer function is said to be a minimal realization of the transfer function.. The realization is called "minimal" because it describes the system with the minimum number of states. The minimum number of state variables required to describe a system equals the order of the differential equation; 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 realization

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).

References

{{math-stub Control theory