Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This is a continuation of our preceding study dealing with robust stabilizing controller synthesis for uncertain discrete-time linear periodic/time-invariant systems. In this preceding study, we dealt with the case where the underlying systems are affected by polytopic-type uncertainties and revealed a particular periodically time-varying dynamical controller (PTVDC) structure that allows LMI-based robust stabilizing controller synthesis. Based on these preliminary results, in this paper, we provide LMI conditions for robust H2 and H∞ PTVDC synthesis. One of the salient features of the proposed method is that we can reduce the conservatism and improve the control performance gradually by increasing the period of the controller to be designed. In addition, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we illustrate that our design method is indeed effective to achieve less conservative results under both the periodic and time-invariant settings. keywords: Robust control, periodic systems, polytopic uncertainties, linear matrix inequalities.

Original languageEnglish
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages5438-5443
Number of pages6
DOIs
Publication statusPublished - Dec 1 2008
Externally publishedYes
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

Fingerprint

Discrete-time Linear Systems
Linear systems
Time-varying
Synthesis
Controller
Controllers
Design Method
Polytopic Uncertainty
Invariant
Time varying systems
Periodic Systems
Robust control
Robust Control
Linear matrix inequalities
Continuation
Matrix Inequality
Linear Inequalities
Discrete-time
Numerical Experiment
Uncertainty

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Ebihara, Y., Peaucelle, D., & Arzelier, D. (2008). Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 5438-5443). [4738716] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4738716

Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. / Ebihara, Yoshio; Peaucelle, Dimitri; Arzelier, Denis.

Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. p. 5438-5443 4738716 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ebihara, Y, Peaucelle, D & Arzelier, D 2008, Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4738716, Proceedings of the IEEE Conference on Decision and Control, pp. 5438-5443, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4738716
Ebihara Y, Peaucelle D, Arzelier D. Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. p. 5438-5443. 4738716. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4738716
Ebihara, Yoshio ; Peaucelle, Dimitri ; Arzelier, Denis. / Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. pp. 5438-5443 (Proceedings of the IEEE Conference on Decision and Control).
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