State-space Representation Of Dynamic Systems ( Forcing Function Does Not Involve Derivative Terms)

State-space representation of nth-order systems of linear differential equations in which the forcing function does not involve derivative terms:

Consider the following nth-order system:

-abIes is quite convenient. Practically, however, because higher-order derivative terms are inaccurate, due to the noise effects inherent in any practical situations, such a choice of the state variables may not be desirable.)

Let us define

The nth-order system can be written as

The output can be given by

Where,  C = [1 0 ... 0]

Note that the state-space representation for the transfer function system