TAILIEUCHUNG - Discrete Time Systems Part 2

Tham khảo tài liệu 'discrete time systems part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 2 Observers Design for a Class of Lipschitz Discrete-Time Systems with Time-Delay Ali Zemouche and Mohamed Boutayeb Centre de Recherche en Automatique de Nancy CRAN UMR 7039 CNRS Nancy-Université 54400 Cosnes et Romain France 1. Introduction The observer design problem for nonlinear time-delay systems becomes more and more a subject of research in constant evolution Germani et al. 2002 Germani Pepe 2004 Aggoune et al. 1999 Raff Allgower 2006 Trinh et al. 2004 Xu et al. 2004 Zemouche et al. 2006 Zemouche et al. 2007 . Indeed time-delay is frequently encountered in various practical systems such as chemical engineering systems neural networks and population dynamic model. One of the recent application of time-delay is the synchronization and information recovery in chaotic communication systems Cherrier et al. 2005 . In fact the time-delay is added in a suitable way to the chaotic system in the goal to increase the complexity of the chaotic behavior and then to enhance the security of communication systems. On the other hand contrary to nonlinear continuous-time systems little attention has been paid toward discrete-time nonlinear systems with time-delay. We refer the readers to the few existing references Lu Ho 2004a and Lu Ho 2004b where the authors investigated the problem of robust Hx observer design for a class of Lipschitz time-delay systems with uncertain parameters in the discrete-time case. Their method show the stability of the state of the system and the estimation error simultaneously. This chapter deals with observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main result lies in the use of a new structure of the proposed observer inspired from Fan Arcak 2003 . Using a Lyapunov-Krasovskii functional a new nonrestrictive synthesis condition is obtained. This condition expressed in term of LMI contains more degree of freedom than those proposed by the approaches available in literature. Indeed these last use a .

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