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 observer-based 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.