Establishing Lipschitz properties of multivariable algebraic loops with incremental sector nonlinearities

In this paper we give a sufficient condition (in terms of an LMI) for the well-posedness of a feedback interconnection between a linear system and an incrementally sector bounded static nonlinearity. In particular, we prove the global invertibility of the algebraic constraint arising from the feedback interconnection and prove a suitable Lipschitz bound for the arising global inverse function. We also comment on the useful ramifications of the proposed condition on LMI- based anti-windup synthesis methods recently proposed in the literature, wherein possible numerical problems arising from solutions which are "almost" non well-posed are ruled out by enforcing a suitable Lipschitz constant on the inverse function.