Update state-space representation by hand

Question

Suppose we have the following state-space representation:

• $x(k + 1) = Ax(k) + Bu(k)$
• $y(k) = Cx(k) + Du(k)$

When calculating the state space by hand, should I use the following procedure?

1. Set k = 0
2. Calculate $x(1)$ using $u(0)$ and $x(0)$
3. Calculate $y(0)$ using $u(0)$ and $x(0)$
4. Set $k = 1$
5. Calculate $x(2)$ using $u(1)$ and $x(1)$
6. Calculate $y(1)$ using $u(1)$ and $x(1)$

Thanks in advance.

Answer 1

Yes. You can do within a for loop if you use a programming software.