For the system shown
x^(˙)=[[0,2],[-3,-5]]x+[[1],[2]]u,y=[[1,1]]x,[[x_(1)(0)],[x_(2)(0)]]=[[0],[0]], and u(t)=0
(a) Obtain
e^(At)
using Cayley-Hamilton. (b) Obtain
e^(At)
by first finding
(sI-A)^(-1)=\Phi (s)
. (c) Evaluate
x(t)
and
y(t)
using time domain approach. (d) Evaluate impulse response of the system,
h(t)
. (e) Evaluate
x(t)
by first obtaining
x(s)
. (f) Evaluate system transfer function
H(s)
.