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A complete and convex search for discrete-time noncausal FIR Zames-Falb multipliers

We propose a convex search for a subclass of discrete-time Zames-Falb multipliers. Specifically we search for noncausal multipliers with FIR (finite impulse response) structure of arbitrary order. The subclass is shown to be phase-equivalent to the class of discrete-time rational noncausal Zames-Falb multipliers. The search can be expressed as an LMI (linear matrix inequality) whose number of parameters increases quadratically with model order and whose number of linear constraints increases linearly with model order. The search may be used both for the case where the nonlinearity is slope-restricted and for the case where the nonlinearity is odd and slope-restricted. We report favourable results with respect to those in the literature.