Low-gain integral control for a class of discrete-time Lur’e systems with applications to sampled-data control

Authors

Chris Guiver, Edinburgh Napier University
Richard Rebarber, University of Nebraska - LincolnFollow
Stuart Townley, University of Exeter

Document Type

Article

Date of this Version

8-8-2022

Citation

Int J Robust Nonlinear Control. 2022;1–28.. DOI: 10.1002/rnc.6455

Comments

Open access.

Abstract

We study low-gain (P)roportional (I)ntegral control of multivariate discrete-time, forced Lur’e systems to solve the output-tracking problem for constant reference signals. We formulate an incremental sector condition which is sufficient for a usual linear low-gain PI controller to achieve exponential disturbance-to-state and disturbance-to-tracking-error stability in closed-loop, for all sufficiently small integrator gains. Output tracking is achieved in the absence of exogenous disturbance (noise) terms. Our line of argument invokes a recent circle criterion for exponential incremental input-to-state stability. The discrete-time theory facilitates a similar result for a continuous-time forced Lur’e system in feedback with sampled-data low-gain integral control. The theory is illustrated by two examples.