From the state model equations, we can derive the transfer function of the system. From definition of transfer function, we can write
For a linear time-invariant system the dynamics can be written in vector differential form as follows:
Taking Laplace transform of Eq. (9.49), we can write
∴ [sI– A] X(s) = BU(s) [Taking x(0) = 0]
∴ X (s) = [sI – A]−1BU(s) (9.51)
Taking Laplace transform of Eq. (9.50) ...