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 noncausal transfer function. By restricting attention to a subset of these multipliers, a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user. A useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities, which is not the case for all classes of Zames–Falb multipliers. [ABSTRACT FROM AUTHOR]