A study on ILC for linear discrete systems with single delay

Abstract

In this article, we utilize a new notation, namely discrete matrix delayed exponential function, to deal with iterative learning control (ILC) problem for linear discrete systems with single delay, which is totally different from the approach in the previous literatures. With the help of a representation of a solution involving discrete matrix delayed exponential function, we can not only present the output clearly on each subinterval determined by the length of time delay, but also we need not to not turn ILC for linear discrete delayed systems to a Roesser model, which is always used to seek the criterion for convergence results. Numerical examples are also presented to verify the theoretical results.

Keywords:

• Linear discrete systems with single delay
• discrete matrix delayed exponential function
• ILC
• convergence

Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. We thank the help from the editor too.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11661016]; Training Object of High Level and Innovative Talents of Guizhou Province [(2016)4006]; Unite Foundation of Guizhou Province [[2015]7640]; Graduate Course of Guizhou University [ZDKC[2015]003]; the Slovak Research and Development Agency [grant number APVV-14-0378]; the Slovak Grant Agency VEGA [grant number 2/0153/16], [grant number 1/0078/17].