  We introduce $(\gamma,\delta)$-similarity, a notion of system comparison that
measures to what extent two stable linear dynamical systems behave similarly in
an input-output sense. This behavioral similarity is characterized by measuring
the sensitivity of the difference between the two output trajectories in terms
of the external inputs to the two potentially non-deterministic systems. As
such, $(\gamma,\delta)$-similarity is a notion that characterizes
\emph{approximation} of input-output behavior, whereas existing notions of
simulation target equivalence. Next, as this approximation is specified in
terms of the $L_2$ signal norm, $(\gamma,\delta)$-similarity allows for
integration with existing methods for analysis and synthesis of control
systems, in particular, robust control techniques. We characterize the notion
of $(\gamma,\delta)$-similarity as a linear matrix inequality feasibility
problem and derive its interpretation in terms of transfer matrices. Our study
on the compositional properties of $(\gamma,\delta)$-similarity shows that the
notion is preserved through series and feedback interconnections. This
highlights its potential application in compositional reasoning, namely
abstraction and modular synthesis of large-scale interconnected dynamical
systems. We further illustrate our results in an electrical network example.
