The following differential equations represent linear timeinvariant systems. Write the dynamic equations (state equations and output equations) in vector- form.

(a) d2 y(t) d1') (t) --+ 4 _. - + (t) = 5 (t) dt2 dt y T

(b) d3 (t) d2 (t) d (t) 2-y- + 3-y- + 5-y- + 2y(t) = r(t) dt3 dt 2 dt

(c) y(T)dT = r-(t)

(d) d4y(t) + ~ d3y(t) + ~ dy(t) + y(t) = 2r(t)

dt4 2 dt 3 2 dt .

Problem