10.3 STATE MODEL OF A SECOND-ORDER SYSTEM
Let us consider the following equation for 2nd order system:
y(k + 2) + 4y(k + 1) + 3y(k) = u(k) (10.6)
In Eq. (10.6) there are two delay elements i.e., y(k + 2) and y(k + 1). Figure 10.4 shows the way of obtaining y(k) from y(k + 2).
From Eq. (10.6) we can write
y(k + 2) = u(k) − 3y(k) −4y(k + 1) (10.7)
Let x1(k) and x2(k) be the output of delay elements of x1(k + 1) and x2(k + 1) respectively.
Figure. 10.5 shows the representation of Eq. (10.7).