Global H∞ controllers for a class of nonlinear systems

In this note, the problem of state feedback H_∞ control for a class of nonlinear systems is considered. The class under study is a generalization of the well-known Lur´e systems. The H_∞ problem is addressed via a class of storage functions of the Lur´e-Postnikov type whose integral term is parameterized by a nonlinear scalar function. The related H_∞ 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 L₂-performance globally. Some guidelines for an effective design of the controller within this set are discussed via two examples.