Find the state vector qt using the Laplace transform method

Find the state vector q(t) using the Laplace transform method:

q\' = Aq + Bx

with:

A = { -1      1}, B= {1    2}, q(0) = { 2 },    and x = { u(t) }

      {0        -2},       {0      3},            { 3 }                   {   0   }

All in MATRIX from .

Solution

MATLAB CODE:

syms s
A=[-1 1;0 -2]
B=[1 2;0 3]
q0=[2;3]
x=[1;0]
qs=inv(s*eye(2)-A)*(q0+B*[1/s;0])
q=ilaplace(qs)