Analysis of Systems With Slope Restricted Nonlinearities Using Externally Positive Zames–Falb Multipliers

This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames-Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive non-causal transfer function. By restricting attention to a sub-set of these multipliers, a set of pure LMI conditions is obtained which requires no initial paramterisation by the user. A useful by-product of using externally positive systems is that the results are applicable to non-odd slope restricted nonlinearities, which is not the case for all classes of Zames-Falb multipliers.