  The concept of dissipativity, as introduced by Jan Willems, is one of the
cornerstones of systems and control theory. Typically, dissipativity properties
are verified by resorting to a mathematical model of the system under
consideration. In this paper, we aim at assessing dissipativity by computing
storage functions for linear systems directly from measured data. As our main
contributions, we provide conditions under which dissipativity can be
ascertained from a finite collection of noisy data samples. Three different
noise models will be considered that can capture a variety of situations,
including the cases that the data samples are noise-free, the energy of the
noise is bounded, or the individual noise samples are bounded. All of our
conditions are phrased in terms of data-based linear matrix inequalities, which
can be readily solved using existing software packages.
