A dynamic system is described by the state-vaTiablc equations :X o= Ax and y = Cx, where and x(O) = [1 2r.

(a) Obtain the state-transition matrix ¢(t).

(b) Find the stat.e vaTiable responses x 1 (t) and x2(t).

(c) Find the output Tesponse y( t).

(d) For this system verify that:

¢(0) =I q;-J (t) ¢( -t)

¢(1)¢(2) = cp(3).

Problem