Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes

C. Bennani; F. Bedouhene; A. Zemouche; H. Bibi; K. Chaib-Draa; A. Aitouche; R. Rajamani

doi:10.23919/ACC.2018.8431745

Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes

C. Bennani
, F. Bedouhene
, A. Zemouche
, H. Bibi
, K. Chaib-Draa
, A. Aitouche
, R. Rajamani

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and 2-bounded disturbances. We propose a new variant of the classical two-steps LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from the stabilization problem by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the H∞ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. Numerical evaluation by Monte Carlo is presented to show the superiority of the proposed Modified Two-Steps Method (MTSM) from LMI feasibility point of view.

Original language	English (US)
Title of host publication	2018 Annual American Control Conference, ACC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4398-4402
Number of pages	5
ISBN (Print)	9781538654286
DOIs	https://doi.org/10.23919/ACC.2018.8431745
State	Published - Aug 9 2018
Event	2018 Annual American Control Conference, ACC 2018 - Milwauke, United States Duration: Jun 27 2018 → Jun 29 2018

Publication series

Name	Proceedings of the American Control Conference
Volume	2018-June
ISSN (Print)	0743-1619

Other

Other	2018 Annual American Control Conference, ACC 2018
Country/Territory	United States
City	Milwauke
Period	6/27/18 → 6/29/18

Bibliographical note

Publisher Copyright:
© 2018 AACC.

Keywords

Linear Matrix Inequalities (LMIs)
Observer-based control
criterion
uncertain systems

Publisher link

10.23919/ACC.2018.8431745

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Bennani, C., Bedouhene, F., Zemouche, A., Bibi, H., Chaib-Draa, K., Aitouche, A., & Rajamani, R. (2018). Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes. In 2018 Annual American Control Conference, ACC 2018 (pp. 4398-4402). Article 8431745 (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431745

Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes. / Bennani, C.; Bedouhene, F.; Zemouche, A. et al.
2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 4398-4402 8431745 (Proceedings of the American Control Conference; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Bennani, C, Bedouhene, F, Zemouche, A, Bibi, H, Chaib-Draa, K, Aitouche, A & Rajamani, R 2018, Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes. in 2018 Annual American Control Conference, ACC 2018., 8431745, Proceedings of the American Control Conference, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 4398-4402, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431745

Bennani C, Bedouhene F, Zemouche A, Bibi H, Chaib-Draa K, Aitouche A et al. Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes. In 2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 4398-4402. 8431745. (Proceedings of the American Control Conference). doi: 10.23919/ACC.2018.8431745

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AB - This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and 2-bounded disturbances. We propose a new variant of the classical two-steps LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from the stabilization problem by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the H∞ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. Numerical evaluation by Monte Carlo is presented to show the superiority of the proposed Modified Two-Steps Method (MTSM) from LMI feasibility point of view.

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Robust H∞ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes

Abstract

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