Robust input-to-output stabilization of nonlinear systems with a specified gain

Robust stabilization of nonlinear systems has been extensively studied subject to both static and dynamic uncertainties. In particular, a class of nonlinear controllers can be explicitly constructed based on recursively applying the small gain theorem. In this paper, we further investigate the so-called robust input-to-output stabilization problem for systems with additional external input (or perturbation, rather than the control input). It aims to explicitly construct a controller such that the system is input-to-output stable (IOS) from the external input to the specified output, moreover, with a specified IOS gain.