Decentralized observers for a class of large-scale singular systems via LMI

Purpose – The purpose of this paper is to propose a decentralized observer for large‐scale singular systems.Design/methodology/approach – In this paper, the authors investigate the problem of observers' design for large‐scale singular systems. The proposed decentralized observer is based on a new parameterization of the generalized Sylvester equation solution. The considered system is partitioned into small‐sizes interconnected subsystems with unknown interconnections.Findings – A decentralized observer based on new parameterization of generalized Sylvester equation. The performance of the proposed approach is illustrated by a numerical example.Originality/value – The proposed approach unites the full‐order, the reduced‐order and the minimal order observer design for large‐scale system. The conditions of the existence of this observer are given in the linear matrix inequalities (LMI) form.

[1]  K. C. Daly.  The computation of Luenberger canonical forms using elementary similarity transformations , 1976 .

[2]  Izumi Masubuchi,et al.  LMI-based controller synthesis: A unified formulation and solution , 1998 .

[3]  Sylviane Gentil,et al.  Commande et régulation par calculateur numérique : de la théorie aux applications , 1977 .

[4]  Chiang-Cheng Chiang,et al.  Adaptive Fuzzy Sliding Mode Control For Time-Delay Uncertain Large-Scale Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  C. Foulard,et al.  Commande Et Regulation Par Calulateur Numerique , 1979 .

[6]  Mohamed Darouach.  Solution to Sylvester equation associated to linear descriptor systems , 2006, Syst. Control. Lett..

[7]  Li Xiaohua,et al.  Organically Structured Control of Large-Scale Systems with Expanding Construction Based on State Observation , 2015 .

[8]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[9]  Mihail M. Konstantinov,et al.  Computational methods for linear control systems , 1991 .

[10]  M. Boutayeb,et al.  Design of observers for descriptor systems , 1995, IEEE Trans. Autom. Control..

[11]  Antonio J. Conejo,et al.  Decomposition Techniques in Mathematical Programming: Engineering and Science Applications , 2006 .

[12]  Zhengrong Xiang,et al.  Non-fragile observer design for nonlinear switched systems with time delay , 2009, Int. J. Intell. Comput. Cybern..

[13]  Bin Jiang,et al.  Nonfragile Observer for Discrete-Time Switched Nonlinear Systems with Time Delay , 2011, Circuits Syst. Signal Process..

[14]  Mohamed Darouach,et al.  Observers for a Class of Nonlinear Singular Systems , 2008, IEEE Transactions on Automatic Control.

[15]  M. Darouach,et al.  Observers for Lipschitz nonlinear descriptor systems: Application to unknown inputs systems , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[16]  D. D. Siljak,et al.  Decentralized Adaptive Control: Structural Conditions for Stability , 1988, 1988 American Control Conference.

[17]  Zhengrong Xiang,et al.  Non-fragile observer for switched non-linear systems with time delay under asynchronous switching , 2011, Int. J. Model. Identif. Control..

[18]  Andrzej J. Osiadacz.  Large‐Scale Control Systems, Theories And Techniques, Magdi S. Mahmoud, Mohamed F. Hassan and Mohamed G. Darwish, Marcel Dekker, 1985 , 2007 .

[19]  Fabien Claveau.  Contribution à l'analyse et la commande structurée des grands systèmes , 2005 .

[20]  Mohammad Aldeen,et al.  Decentralised observer-based control scheme for interconnected dynamical systems with unknown inputs , 1999 .

[21]  D. P. Mital,et al.  Decentralized robust controller design for a class of interconnected uncertain systems: with unknown bound of uncertainty , 1996, IEEE Trans. Autom. Control..

[22]  Dragoslav D. Šiljak,et al.  Large-Scale Dynamic Systems: Stability and Structure , 1978 .

[23]  André Bassong Onana.  Filtrage optimal des systèmes dynamiques linéaires discrets : décentralisation et robustesse numérique , 1992 .

[24]  Mohamed Darouach,et al.  Optimal unbiased reduced order filtering for discrete-time descriptor systems via LMI , 2009, Syst. Control. Lett..