Obtain a state-space representation for a system whose differential equation is given by

·:r· + 3x + 3x + x = u + u, where the output is y = x.

(a) Use this result to determine the system transition matrix ¢(t) and

¢(s).

(b) Use Ackermann's formula to determine the controller K that places the roots of this system at -1,-2 ± 2j.

Problem