Abstract
The class of O’Shea–Zames–Falb multipliers currently yields the strongest known results for establishing the absolute stability of feedback interconnections between linear time-invariant (LTI) systems and slope-restricted nonlinearities. In the discrete-time setting, these multipliers are known to fully characterize the class of such nonlinearities, motivating the following conjecture: O’Shea–Zames–Falb multipliers are both necessary and sufficient for absolute stability.
This talk will begin with a concise overview of absolute stability theory. We will then present recent advances, including the construction of destabilizing nonlinearities when the existence of an O’Shea–Zames–Falb multiplier can be ruled out via duality-based arguments. Finally, we will discuss current challenges and limitations that remain in resolving this conjecture definitively.
Biographical Information
Dr. Joaquin Carrasco is a Reader in Control Systems at the Department of Electrical and Electronic Engineering, University of Manchester, UK. Born in Abaran, Spain in 1978, he earned a BSc in Physics and a PhD in Control Engineering from the University of Murcia in 2004 and 2009, respectively.
After completing a postdoctoral position at Leibniz Universität Hannover (2009–2010), he joined the Control Systems Centre at Manchester in 2010 as a research associate. Since November 2011, he has been a member of the academic staff and is currently appointed as Reader in Control Systems.