1. Consider a system with state-space model:
+
u
.y=
Solution:
.u(t) = r(t) –K x(t)
The characteritics equation of the closed –loop sysem
.We have :
A=
;B=
C=[1 0 0] ;
The characteristic equation of the closed –loop system:
.det [sI-A+BK] = 0
 det

=0
(5+ )+s(3+ )+(2+ ) =0 (1)
The desired characteristic equation:
(s+4.8)(
) =0
+105.08s+283.2 =0
(2)
the coefficients of the equation (1) and (2) :
=>

2. Conclution : K=[ 281.2 102.08 9.4]