Global inverse optimal design of ISS controllers with backstepping approach

In this paper, the problem of input-to-state stability(ISS) of a class of nonlinear system which can be transformed into the strict feedback form is considered, the stable controller is designed by employing a new backstepping procedure and inverse optimal approach. The main tools in our analysis are Legendre-Fenchel transformations, the theory of convex function and Young´s inequality.