New decentralized control design for interconnected nonlinear discrete-time systems with nonlinear interconnections

This paper deals with a new decentralized observer-based controller design method for nonlinear discrete-time interconnected systems with nonlinear interconnections. Thanks to some algebraic transformations and the use of a new variant of Young's inequality, an LMI-based approach is provided to compute the observer-based controller gain matrices. Furthermore, the congruence principle is used under a judicious and new manner leading to include additional slack variables and to cancel some bilinear matrix coupling. The effectiveness of proposed methodology is shown through an illustrative example.

[1]  Ali Zemouche,et al.  Observers for a class of Lipschitz systems with extension to Hinfinity performance analysis , 2008, Syst. Control. Lett..

[2]  P.R. Pagilla,et al.  A decentralized output feedback controller for a class of large-scale interconnected nonlinear systems , 2005, Proceedings of the 2004 American Control Conference.

[3]  Hisham M. Soliman,et al.  Resilient guaranteed cost control of a power system , 2014, Journal of advanced research.

[4]  Angelo Alessandri,et al.  A new LMI condition for decentralized observer-based control of linear systems with nonlinear interconnections , 2014, 53rd IEEE Conference on Decision and Control.

[5]  Lin Huang,et al.  Design of nonlinear interconnections guaranteeing the absence of periodic solutions , 2006, Syst. Control. Lett..

[6]  Prabhakar R. Pagilla,et al.  Decentralized output feedback control of a class of large-scale interconnected systems , 2007, IMA J. Math. Control. Inf..

[7]  Masao Ikeda,et al.  Decentralized stabilization for expanding construction of large-scale systems , 1990 .

[8]  Ali Zemouche,et al.  A robust ℋ∞ observer‐based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities , 2016 .

[9]  Bertrand Grandvallet,et al.  New LMI Condition for Observer-Based HINFINITY Stabilization of a Class of Nonlinear Discrete-Time Systems , 2013, SIAM J. Control. Optim..

[10]  Ian R. Petersen,et al.  Decentralized state feedback stabilization and control of uncertain large scale systems with integrally constrained interconnections , 1998 .

[11]  Jianming Lian,et al.  Reduced-order observer-based decentralised control of non-linear interconnected systems , 2009, Int. J. Control.

[12]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

[13]  Angelo Alessandri,et al.  Observer-based stabilisation of linear systems with parameter uncertainties by using enhanced LMI conditions , 2015, Int. J. Control.

[14]  Jianming Lian,et al.  Decentralized Dynamic Output Feedback Control of Nonlinear Interconnected Systems , 2010, IEEE Transactions on Automatic Control.

[15]  N. Braiek,et al.  Decentralized Observer based Guaranteed Cost Control for Nonlinear Interconnected Systems , 2009 .

[16]  I. Petersen,et al.  Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[17]  Michel Zasadzinski,et al.  H∞ circle criterion observer design for Lipschitz nonlinear systems with enhanced LMI conditions , 2016, 2016 American Control Conference (ACC).

[18]  Srdjan S. Stankovic,et al.  Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems , 2007, Autom..

[19]  Bahram Shafai,et al.  Decentralized PI observer-based control of nonlinear interconnected systems with disturbance attenuation , 2011, Proceedings of the 2011 American Control Conference.