Decentralized Robust H∞ Control of Large Scale Systems with Polytopic-Type Uncertainty

Amal Zouhri; Ismail Boumhidi

doi:10.15866/ireaco.v9i2.8728

Decentralized Robust H∞ Control of Large Scale Systems with Polytopic-Type Uncertainty

Amal Zouhri^(1*), Ismail Boumhidi⁽²⁾

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/ireaco.v9i2.8728

Abstract

In this article, we present a decentralized robust stabilization and H∞ control for large-scale uncertain systems. The system is represented by a set of interconnected subsystems. We interest to the study of stability of the global system in closed loop using state feedback decentralized controllers. The stability conditions are presented in terms of LMI. In order to improve this first approach, we propose, through a criterion H∞, to study the robustness according the effects of interconnections between the subsystems. Some sufficient conditions, ensuring all the closed-loop stability, are supplied in terms of Linear Matrix Inequalities (LMIs) and the feedback gain matrix of each local controller is obtained by solving the LMIs. Finally, the practice examples are given to illustrate the efficiency of the proposed approach.
Copyright © 2016 Praise Worthy Prize - All rights reserved.

Keywords

Decentralized Control; Large-Scale System; Linear Matrix Inequality (LMI); Uncertain Systems

Full Text:

PDF

References

D.D Siljak, Decentralized Control of Complex Systems. Academic Press, 1991.
http://dx.doi.org/10.1016/s0076-5392(08)63418-9

M.S. Mahmoud, N.B. Almutairi, Resilient decentralized stabilization of interconnected time- delay systems with polytopic uncertainties, Int. J. Robust. Nonlinear Control, Vol. 21: pp. 355-372, 2011
http://dx.doi.org/10.1002/rnc.1594

A. Zouhri, M. Benyakhlef, S. Kririm, and I. Boumhidi, Robust Stability and H∞ Analysis for Interconnected Uncertain Systems, International Journal of Mathematics and Statistics™, ISSN 0974-7117 (Print), ISSN: 0973-8347 (Online), Vol. 17(Issue 1): 55-66, 2016.

Rajaa Vikhram, G.Y., Latha, S., Robust shunt FACTS controller design for power system damping improvement, (2013) International Review of Electrical Engineering (IREE), 8 (2), pp. 792-801.

Widyan, M.S., Operational performance of synchronous generator hybrid-excited by pmdc and pv generators, (2014) International Review of Electrical Engineering (IREE), 9 (4), pp. 863-872.
http://dx.doi.org/10.15866/iree.v9i4.2472

S. Schuler, U. Münz, F. Allgöwer, Decentralized state feedback control for interconnected systems with application to power systems, Journal of Process Control, Vol. 24: 379–388, 2014.
http://dx.doi.org/10.1016/j.jprocont.2013.10.003

T. N. Lee, and U. L. Radovic, Decentralized Stabilization of Linear Continuous and Discrete- Time Systems with Delays in Interconnections, IEEE Transactions on Automatic Control, Vol. 33: 757–761, 1988.
http://dx.doi.org/10.1109/9.1293

A. Zouhri and I. Boumhidi, Decentralized control of interconnected systems with time-delays, 12th ACS/IEEE International Conference on Computer Systems and Applications AICCSA 2015 November 17-20, 2015, Marrakech, Morocco.

M.S. Mahmoud, N.B. Almutairi, Decentralized Stabilization of Interconnected Systems with Time-varying Delays, European Journal of Control, Vol. 6: 624–633, 2009.
http://dx.doi.org/10.3166/ejc.15.624-633

B. Xu, On Delay-Independent Stability of Large-Scale Systems with Time Delays, IEEE Transactions on Automatic Control, Vol.40: 930–933, 1995.
http://dx.doi.org/10.1109/9.384233

S. Boyd, L. E. Ghaoui, E. Feron and Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, Vol. 15, 1994.
http://dx.doi.org/10.1137/1.9781611970777

A. Zouhri, M. Benyakhlef and I. Boumhidi, Finite Frequency H- /H∞ Stability of Singularly Perturbed Systems, WSEAS Transactions on Systems and Control, E-ISSN: 2224-2856, Vol. 9:302-308, 2014.

R. Mohanty Soumya, K. Nand, K. Ray Prakash, Robust H-infinite loop shaping controller based on hybrid PSO and harmonic search for frequency regulation in hybrid distributed generation system, International Journal of Electrical Power & Energy Systems, Vol 60: pp. 302-316, September 2014.
http://dx.doi.org/10.1016/j.ijepes.2014.03.012

Z. Duan, L. Huang, L. Wang, J. Wang, Some applications of small gain theorem to interconnected systems, Systems & Control Letters , Vol 52: pp. 263 – 273, 2004.
http://dx.doi.org/10.1016/j.sysconle.2004.02.004

F. Zhou et al., Fuzzy Decentralized Control for a Class of Networked Systems with time delay and missing measurements, Asian Journal of Control, Vol. 17, No. 1: pp. 84–98, January 2015.
http://dx.doi.org/10.1002/asjc.1070

B. Olivier, Notions de base pour une initiation à la synthese robuste de correcteurs par approche LMI (3, 2008).

Y. Zhang and A. H. Pheng, Stability of fuzzy control systems with bounded uncertain delays, IEEE Trans. Fuzzy Syst., Vol. 10: 92–97, 2002.
http://dx.doi.org/10.1109/91.983283

P. Gahinet, A. Nemirovski, A. Laub, and M., Chilali, LMI Control Toolbox User’s Guide, Mathworks, Natick, Massachusetts, (1995).

Refbacks

There are currently no refbacks.

Username
Password
Remember me