Incremental gain analysis of piecewise linear systems and application to the antiwindup problem (Q1301441)

The paper deals with feedback systems with saturating actuators. It presents an approach to estimating the \(L_2\) incremental gain, which is a possible generalization of the \(H^\infty\) norm to nonlinear systems. The main contribution of the result lies in the use of the incremental gain as a performance criterion and a derivation for general piecewise linear continuous-time systems. The technique for bounding above the incremental gain uses storage functions, which satisfy a dissipation property, deriving a set of linear matrix inequalities. The application of the results to the antiwindup problem is illustrated by examples.