Robust nonlinear control based on norm-bounded approximation and gain-scheduling

A well-known drawback of classical gain-scheduling methods is that they provide controllers which require to be checked after their synthesis: the immersion of a nonlinear system into a family of linear systems to build local control laws provides a global control law only effective on neighbourhoods. The aim of this paper is to expose a general algorithm able to provide a global control law which guarantees a global transition between two working points of a given nonlinear system, under nonlinear parametrical uncertainties. A linear approximation method of a nonlinear function on a given domain is exposed. The example of a levitating ball system illustrates the controller design. Conservatism is shortly discussed.