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 [*z***I** − **A**]*z*

= *z*^{−1}[*z***I** − **A**]^{−1} = state transition matrix.

The expression *z* ^{–1}[*z***I** – **A**] ^{–1} can also be compared with resolvent matrix with the linear case where it is [*s***I** – **A**] ^{–1}. In this case it is multiplied by *z* and we then take the inverse to get state transition matrix.

**Proof:**

The *z*–transform of Eq. (10.18) ...

Start Free Trial

No credit card required