This work is devoted to the remote feedback control of a linear process with "Internet in the loop". In such a networked control situation, variable and unpredictable delays arise, which may decrease the global performance and, in the extreme, destabilize the system. Our aim is to obtain the best performance (here, the exponential stability rate) despite the variation of the network QoS (quality of service). The considered application is based on a Master-Slave structure. The Slave is a light mobile robot, that receives control data and sends its sampled output (position) via a UDP protocol (indeed, packet re-emission of an old output sample is not needed). A Master computer realizes the remote control, the design of which is based on a remote observer achieving a state prediction of the Slave despite the variable delays and possible packet losses. Using time-stamped packets, the Master also detects the network QoS by estimating the variable time delays. It then uses this information so to adapt its observer/controller gains and guarantee the best possible decay rate. The design of this gain scheduling strategy relies on Lyapunov-Krasovskii functionals with an LMI optimization. Experimental results are provided.