Validity domain estimation for a class of nonlinear H∞ controllers

The problem of estimating the domain of validity of state feedback H_∞ controllers for a class of nonlinear systems is considered. Such a class is a generalization of the well-known Lur´e systems. A class of storage functions of the Lur´e-Postnikov type depending on a free scalar parameter is considered. For each value of this parameter, a tight estimation of the validity domain of the H_∞ controller corresponding to the storage function is provided in form of a strip in the state space. The analytical expression of such estimation makes it possible to compare the performance of the obtained controllers. In particular, some conditions ensuring that nonlinear controllers guarantee larger validity domain estimations than linear controllers are given