Stability and convergence properties of forced Lur'e systems

Abstract

We investigate stability and convergence properties of forced Lur'e systems, that is, systems comprising a linear system in the forward path, a static nonlinearity in the feedback path and a forcing or input. In both the finite- and infinite-dimensional settings, we develop various sufficient conditions for when such systems are input-to-state stable, incrementally input-to-state stable, and exhibit the converging-input converging-state property. We also study the effect that asymptotically almost periodic inputs have on corresponding state and output trajectories of the aforementioned systems. Finally, we note that we consider very general versions of forced Lur'e systems, and so we are able
to apply our results to a variety of applications. For instance, we deduce stability and convergence properties of `four-block' Lur'e systems, which are forced Lur'e systems where the input and output spaces are split in two and only one part of the output is utilised for feedback and is fed back into one part of the input. We also deduce stability properties of sampled-data integral control systems.

Date of Award	13 May 2020
Original language	English
Awarding Institution	University of Bath
Supervisor	Hartmut Logemann (Supervisor) & Christopher Guiver (Supervisor)