Since this is a linear dynamic system described in state-space, the output can be found using the dsolve() command.
syms w(t) x(t) y(t) z(t)
%% State equations
eqns = [diff(w,t) == - 0.00022074*w + 0*x - 0.321386*y + 0.0000004924*z,
diff(x,t) == 0.00012074*w - 0.187744*x + 0.321385*y + 0*z,
diff(y,t) == 0*w + 0.187644*x - 0.321215*y + 0*z,
diff(z,t) == 0*w + 0*x + 0.318725*y - 0.0001005*z];
%% General solution (if initial condition is unknown)
Gsol = dsolve(eqns, 'MaxDegree', 4)
%% Particular solution (if initial condition is known)
cond = [w(0) == 1,
x(0) == 0,
y(0) == 0,
z(0) == 0];
Psol = dsolve(eqns, cond, 'MaxDegree', 4)
