An algorithm to compute multipliers for repeated monotone nonlinearities

A MIMO negative feedback interconnection of a discrete-time LTI system and a repeated time-invariant, monotone nonlinearity are considered. Kulkarni and Safonov (2001) derived the largest class of multipliers that can be used to show stability of such feedback systems. This paper demonstrates in a simple way that these multipliers can be computed efficiently from the solution of a linear matrix inequality (LMI). It is also shown how the structure of the problem can be exploited to reduce its complexity.