  This paper introduces a computational framework to identify nonlinear
input-output operators that fit a set of system trajectories while satisfying
incremental integral quadratic constraints. The data fitting algorithm is thus
regularized by suitable input-output properties required for system analysis
and control design. This biased identification problem is shown to admit the
tractable solution of a regularized least squares problem when formulated in a
suitable reproducing kernel Hilbert space. The kernel-based framework is a
departure from the prevailing state-space framework. It is motivated by
fundamental limitations of nonlinear state-space models at combining the
fitting requirements of data-based modeling with the input-output requirements
of system analysis and physical modeling.
