i(t) = Ar(t) + bu(t),
y(t) = cx(t),
where x(t) = R³, u(t) = R, and y(t) = R;
2.75
0.25 0.625
1 2 0.5
1.5 -1.5 1.25
A =
b = (1, 2, -2),
and c= (-0.5, 0.5, 0.25).
Compute a matrix V € R³x3 whose columns provide the Kalman decomposition of the
system; compute à := V-¹AV, 6 = V-¹b, and c = cV; and use the Kalman decomposition
to derive the input-output transfer function of the system.
Fig: 1