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On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities

This paper shows that the intractable Zames-Falb multiplier problem can be cast as a convex optimisation problem. It has attracted significant academic interest from the control research community, notably from Heath and Lanzon's group in Manchester (William.Heath@manchester.ac.uk, Alexander.Lanzon@manchester.ac.uk). It has been useful in the non-conservative analysis of anti-windup schemes for complex systems and has been exploited during the £178K MoD/DGA funded project "Dynamic Controllers" (Domain Lead Graham Wallis, graham.wallis@mbda-systems.com). With this work, it was shown that a missile autopilot with appropriately designed anti-windup and 1/6 of the nominal control capacity could function as well as the nominal un-augmented autopilot.