# ADAPTIVE MIMO MULTI-PERIODIC REPETITIVE CONTROL SYSTEM: LIAPUNOV ANALYSIS

### H. Dang, D. H. Owens

#### Abstract

This paper presents a simple feed forward adaptive multi-periodic repetitive control scheme for the ASPR(Almost Strictly Positive Real) or ASNR(Almost Strictly Negative Real, See Appendix for definition) plant to asymptotically track/reject multi-periodic reference/disturbance signals. The lyapunov stability analysis is given. This is an extension work of the lyapunov stability analysis for multi-periodic repetitive control system under a positive real condition. A simulation is included. The extension of the lyapunov stability analysis to ASPR or ASNR plant under certain non-linear perturbations and an exponential stability scheme are discussed as well. Finally an adaptive proportional plus multi-periodic repetitive control scheme is proposed.

#### References

- A., I. (1993). Non-Identi er-Based High-Gain Adaptive Control, Lecture Notes in Control and Information Sciences 189. Springer-Verlag, London, 1st edition.
- Dixon W. E., Zergeroglu E., D. D. C. B. (Sep, 2001). Repetitive learning control: A lyapunov-based approach. In Proceedings of the 2001 International Conference on Control Applications, Mexico City, Mexico.

#### Paper Citation

#### in Harvard Style

Dang H. and H. Owens D. (2004). **ADAPTIVE MIMO MULTI-PERIODIC REPETITIVE CONTROL SYSTEM: LIAPUNOV ANALYSIS** . In *Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: Special Session on Analytical and Simulation Methods for Complex Systems, (ICINCO 2004)* ISBN 972-8865-12-0, pages 249-256. DOI: 10.5220/0001129102490256

#### in Bibtex Style

@conference{special session on analytical and simulation methods for complex systems04,

author={H. Dang and D. H. Owens},

title={ADAPTIVE MIMO MULTI-PERIODIC REPETITIVE CONTROL SYSTEM: LIAPUNOV ANALYSIS},

booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: Special Session on Analytical and Simulation Methods for Complex Systems, (ICINCO 2004)},

year={2004},

pages={249-256},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001129102490256},

isbn={972-8865-12-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: Special Session on Analytical and Simulation Methods for Complex Systems, (ICINCO 2004)

TI - ADAPTIVE MIMO MULTI-PERIODIC REPETITIVE CONTROL SYSTEM: LIAPUNOV ANALYSIS

SN - 972-8865-12-0

AU - Dang H.

AU - H. Owens D.

PY - 2004

SP - 249

EP - 256

DO - 10.5220/0001129102490256