In systems theory, a realization of a state space model is an implementation of a given input-output behavior.

Any given transfer function which is strictly proper can easily be transferred into state-space.

In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator. A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.

The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.

controllable canonical form is also known as phase variable canonical form, because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state).

The transfer function coefficients can also be used to construct another type of canonical form

observable canonical form because the resulting model is guaranteed to be observable (i.e., because the output exits from a chain of integrators, every state has an effect on the output).

Students will be able to find transfer function of the system from its state model. Various types of realization such as controllable canonical realization, Observable canonical realization , Jordon realization and particulars of each type. To draw state diagram for each type of realization.