Our aim is to propose an extension of nD systems by treating uncertain parameters of a system as additional independent variables. We recall known results on deriving equations for the sensitivity of the system state to parameter changes. Then, the problem of optimal control of linear systems extended by sensitivity equations with the quadratic criterion is stated. Its solution is relatively easy using the well known results for LQ optimal systems, but in our case the optimal controller is fed additionally by sensitivity signals. A numerical example indicates that the behavior of control system with reduced sensitivity is different than the behavior of classical systems, which is the price that we pay for parameter uncertainty.