ABSTRACT
In this chapter, we will adopt the analog erasure model to describe the communication channel present inside a control loop. This model, also referred to as the packet erasure or packet loss model, can be described as follows [8]. The channel operates in discrete time steps. At every time step, the channel accepts as input a finite-dimensional real vector r(k). The value of the output of the channel y(k) is chosen according to an erasure process. At every time step, the erasure process assumes either the value T or the value R. If the value at time k is T , y(k+ 1) = r(k) and a successful transmission is said to have occurred. Otherwise, y(k+ 1) = φ and an erasure event, or a packet loss, is said to have occurred at time k. The symbol φ denotes that the receiver does not receive any data; however, the receiver is aware that an erasure event has occurred at that time. Note that we have assumed that the channel introduces a constant delay of one time step.
