  The use of persistently exciting data has recently been popularized in the
context of data-driven analysis and control. Such data have been used to assess
system theoretic properties and to construct control laws, without using a
system model. Persistency of excitation is a strong condition that also allows
unique identification of the underlying dynamical system from the data within a
given model class. In this paper, we develop a new framework in order to work
with data that are not necessarily persistently exciting. Within this
framework, we investigate necessary and sufficient conditions on the
informativity of data for several data-driven analysis and control problems.
For certain analysis and design problems, our results reveal that persistency
of excitation is not necessary. In fact, in these cases data-driven
analysis/control is possible while the combination of (unique) system
identification and model-based control is not. For certain other control
problems, our results justify the use of persistently exciting data as
data-driven control is possible only with data that are informative for system
identification.
