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

Guiver, Chris; Rebarber, Richard; Townley, Stuart

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.

Citation

Guiver, C., Rebarber, R., & Townley, S. (2023). Low-gain integral control for a class of discrete-time Lur'e systems with applications to sampled-data control. International Journal of Robust and Nonlinear Control, 33(3), 1410-1437. https://doi.org/10.1002/rnc.6455

• Journal Article Type: Article
• Acceptance Date: Aug 8, 2022
• Online Publication Date: Nov 22, 2022
• Publication Date: 2023-02
• Deposit Date: Aug 9, 2022
• Publicly Available Date: Nov 22, 2022
• Print ISSN: 1049-8923
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 3
• Pages: 1410-1437
• DOI: https://doi.org/10.1002/rnc.6455
• Keywords: discrete-time, input-to-state stability, low-gain integral control, Lur’e systems, sampled-data control
• Public URL: http://researchrepository.napier.ac.uk/Output/2895254