We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth-limited communication network using adaptive sampling intervals. The controller is centralized and not only computes at every sampling instant the new control command for a process but also decides the time interval to wait until taking the next sample.The approach relies on model predictive control ideas, where the cost function penalizes the state and control effort as well as the time interval until the next sample is taken. The latter is introduced to generate an adaptive sampling scheme for the overall system such that the sampling time increases as the norm of the system state goes to zero. This paper presents a method for synthesizing such a predictive controller and gives explicit sufficient conditions for when it is stabilizing. Further explicit conditions are given that guarantee conflict free transmissions on the network. It is shown that the optimization problem may be solved offline and that the controller can be implemented as a lookup table of state feedback gains. The simulation studies which compare the proposed algorithm to periodic sampling illustrate potential performance gains.