  For the class of nonlinear input-affine systems with polynomial dynamics, we
consider the problem of designing an input-to-state stabilizing controller with
respect to typical exogenous signals in a feedback control system, such as
actuator and process disturbances. We address this problem in a data-based
setting when we cannot avail ourselves of the dynamics of the actual system,
but only of data generated by it under unknown bounded noise. For all dynamics
consistent with data, we derive sum-of-squares programs to design an
input-to-state stabilizing controller, an input-to-state Lyapunov function and
the corresponding comparison functions. This numerical design for
input-to-state stabilization seems to be relevant not only in the considered
data-based setting, but also in a model-based setting. Illustration of
feasibility of the provided sum-of-squares programs is provided on a numerical
example.
