10.7 SOLUTION OF STATE EQUATION
The two methods to solve the state equations (i) z –transform method and (ii) series expansion method will be discussed in this article.
10.7.1 z-Transform Method
The solution of state equation of a discrete system is given by
where ϕ (k) = Inverse z–transform of [zI − A]z
= z−1[zI − A]−1 = state transition matrix.
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.
Proof:
x (k + 1) = Ax (k) + Bu(k) (10.18)
The z–transform of Eq. (10.18) ...
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