In this note we examine the solution and the impulsive behaviour of autonomous linear multivariable systems whose pseudo-state beta(t) obeys a linear matrix differential equation A(rho)beta(t)= 0 where A(rho) is a polynomial matrix in the differential operator rho := d/dt. We thus generalize to the general polynomial matrix case some results obtained by Verghese and colleagues which regard the impulsive behaviour of the generalized state vector x(t) of input free generalized state space systems.