Global H/sub (infinity)/ controllers for a class of nonlinear systems

In this note, the problem of state feedback H/sub (infinity)/ control for a class of nonlinear systems is considered. The class under study is a generalization of the well-known Lurʹe systems. The H/sub (infinity)/ problem is addressed via a class of storage functions of the Lurʹe-Postnikov type whose integral term is parameterized by a nonlinear scalar function. The related H/sub (infinity)/ controllers consist of a linear term, which is designed for the underlying linearized system, plus a nonlinear term which depends on the nonlinear function. A simple geometrical criterion is provided for the characterization of the set of controllers which ensure a given level of L/sub 2/-performance globally. Some guidelines for an effective design of the controller within this set are discussed via two examples.