Multivariable algebraic loops with complementarity constraints enforcing some KKT conditions

In this paper, we address the wellposedness and online resolution of algebraic loop arising from the feedback interconnection of a linear time invariant system and a static nonlinearity whose input-output characteristics enforce some KKT optimality conditions. We establish sufficient conditions for the wellposedness of such algebraic loops using the theory of linear complementarity problems. In particular, we show that wellposedness is equivalent to the existence and uniqueness of solution of a convex optimization problem for which efficient solution algorithms are well established. The application of the results to constrained control problem is illustrated using a multivariable antiwindup design.