The jumping process \(\{\sigma(t); t \ge 0 \}\) is a continuous-time discrete-state homogeneous Markov process. The control system is \[ \frac{\partial \xi}{\partial t}(x, t) = \Theta_{\sigma(t)} \frac{\partial \xi}{\partial x}(x, t)\quad (0 \le x \le 1, \ t \ge 0) \tag{1} \] with \(\xi(x, t) = [\xi_1(x, t), \dots ,\xi_n(x, t)]^T\) and boundary conditions \[ \begin{bmatrix} \xi_{-}(1, t) \\ \xi_{+}(0, t) \end{bmatrix} = T_{\sigma(t)}\begin{bmatrix} \xi_{-}(0, t) \\ \xi_{+}(1, t) \end{bmatrix} + u(t) + D_{\sigma(t)} X(t) \tag{2} \] where \[ X'(t) = A_{\sigma(t)} X(t) + B_{\sigma(t)}w(t) \, , \quad w'(t) = S_{\sigma(t)}w(t) \, . \tag{3} \] For each value of \(\sigma(t)\) the matrix \(\Theta_{\sigma(t)}\) is diagonal and the decomposition \([\xi_1(x, t), \dots ,\xi_n(x, t)] = [\xi_{-}(x, t), \xi_{+}(x, t)]\) is determined by the negative and positive elements of the diagonal of \(\Theta_{\sigma(t)}.\) The observer is \(y(t) = C \xi_{+}(1, t).\) The authors set up a feedback by incorporating functions of the observer on the right side of (1) and of both equations (3) and study mean square exponential stability of the closed loop system. The results are applied (numerics included) to a model of freeway traffic control.