Perturbations in distributed parameters control systems (Q1118561)

We consider the control processes \[ (E)\quad z_{xy}+A(x,y)z_ x+B(x,y)z_ y+C(x,y)z=F(x,y)U(x,y)\quad and \] \[ (\bar E)\quad z_{xy}+\bar A(x,y)z_ x+\bar B(x,y)z_ y+\bar C(x,y)z=\bar F(x,y)U(x,y), \] where all functions are defined in \(R=[0,\alpha [\times [0,\beta [\). We show that under appropriate assumptions on the data A, B, C, F, if the process (E) is completely controllable, then the perturbed process \((\bar E)\) is completely controllable too. The result is obtained proving for the evolution matrix V, a continuous dependence on the coefficients A, B, C.