On the existence of multipliers for MIMO systems with repeated slope-restricted nonlinearities

This paper studies the absolute stability problem for closed-loop systems containing a known linear-time-invariant (LTI) part and a static nonlinear element with restricted slope. LMI-based conditions which can be used to guarantee the stability of the closed-loop system are derived, based on extensions of the Zames-Falb multiplier. The paper extends previous single-input-single-output results to multiple-input-multiple-output systems. The generality of the Zames-Falb mulitiplier ensures that it is no more conservative than the Circle and Popov criteria, and sometimes dramatically less so.