{{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]}

{a*x1'[t]+b*x2'[t]==e*u1[t]+f*u2[t], c*x1'[t]+d*x2'[t]==g*u1[t]+h*u2[t]}