On the necessity and sufficiency of discrete-time O’Shea–Zames–Falb multipliers

This paper considers the robust stability of a discrete-time Lurye system consisting feedback interconnection between linear and bounded monotone nonlinearity. It has been conjectured that existence suitable time-invariant (LTI) O’Shea–Zames–Falb multiplier is not only sufficient but also necessary. Roughly speaking, successful proof conjecture would require: (a) conic parameterisation set multipliers describes exactly nonlinearities, (b) lossless S-procedure to show non-existence implies uniformly robustly stable over (c) in used an LTI multiplier. We investigate these three steps, showing current bottlenecks for proving this conjecture. In addition, we provide extension class which may be disprove