This work concerns the control, the observation and then, the implementation principles of a remote system (Master and Slave parts) through the Internet network. This communication link introduces variable delays that have to be taken into account in the control-observation loop. The data-sampling effects will also be considered, even in the aperiodic case. The Slave part is considered to be a linear system. But, since its computation power is supposed to be limited, the control complexity (which, here, is an observerbased state feedback) has to stay in the Master part. The global system must ensure speed performance whatever the delay variation. Such a performance is obtained by showing the robust, exponential stability property, which is proven by using adequate Lyapunov-Krasovskii functionals. This makes possible to compute the controller and observer gains by using LMI optimization. The technical solution we propose is based on a GPS system, which guarantees the Master and Slave clocks to be synchronized. Then, the control and measurement packets are sent together with time-stamps that allow for reconstructing a non-symmetric delay information. It means that Master-to-Slave and Slave-to-Master delays are separately reconstructed by the system (and not only the global RTT, round-trip-time). The last part of the paper provides an example where the Slave is a second-order system.