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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

Authors

Richard Rebarber

Stuart Townley



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
Electronic ISSN 1099-1239
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

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