Building 53, room 4025
Speaker: Prof Will Heath, Bangor University
Title: What can’t you do with OZF multipliers?
Abstract: The O’Shea-Zames-Falb (OZF) multipliers preserve the positivity of monotone nonlinearities. They are an effective tool for analysing the L2 input-output stability of Lurye systems with slope-restricted nonlinearities such as saturation and deadzone.
In this talk we put the case for parameterising them in delay form – and in particular expressing each multiplier as a positive sum of delta operators. This perspective leads naturally to a frequency domain interpretation, expressed as phase limitations on the class of multipliers.
We also consider the behaviour of Lurye systems when the excitation is outside L2: for example, noise, step signals and sine waves. The L2 gain also bounds the power amplification. The existence of a suitable OZF multiplier guarantees a unique steady-state map so that L2 variation (or power) can be measured around the steady state value (or mean). This does not extend to the class of OZF multipliers that require the nonlinearity to be odd. If the excitation is periodic then the system may have multiple attractive limit cycles including subharmonic responses. A subset of the OZF multipliers, together with further technical detail, guarantees good behaviour.
Bio: William Heath received an M.A. in mathematics from the University of Cambridge, U.K. and both an M.Sc. and Ph.D. in systems and control from the University of Manchester Institute of Science and Technology, U.K. He is Head of School of Computer Science and Engineering at Bangor University and Chair of the UK Automatic Control Council. He has previously held positions at the University of Manchester, at the University of Newcastle (Australia) and at Lucas Automotive. His research interests include absolute stability, multiplier theory, constrained control, and system identification.