State-space Representation Of Dynamic Systems ( Forcing Function Does Involving Derivative Terms)

State-space representation of nth-order systems of linear differential equations in which the forcing function involves derivative terms:

With this choice of state variables the existence and uniqueness of the solution of the state equation is guaranteed. (Note that this is not the only choice of a set of state variabIes.) With the present choice of state variables, we obtain

The output equation can be written as