The two methods to solve the state equations (i) z –transform method and (ii) series expansion method will be discussed in this article.
The solution of state equation of a discrete system is given by
where ϕ (k) = Inverse z–transform of [zI − A]z
The expression z –1[zI – A] –1 can also be compared with resolvent matrix with the linear case where it is [sI – A] –1. In this case it is multiplied by z and we then take the inverse to get state transition matrix.
The z–transform of Eq. (10.18) ...