Observers for linear time-varying systems

In a general sense, observation is the problem of finding estimates for the current values of a set of signals given the current and the past values of another set of signals, where both signal sets are interconnected by the action of a dynamical system. In the work of Luenberger [6, 7] a method is described how this can be done in the context of linear time-invariant control systems, where the observed signals are the input and the output and the to be estimated signals are (parts of) the state. The main idea is to feed the observed signals into an auxiliary system, the observer, and to use its output as the desired estimate.