New unified H∞ dynamic observer design for linear systems with unknown inputs

In this paper, a unified H ∞ dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional observer (PO), the proportional integral observer (PIO) and the dynamic observer (DO). The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error. A numerical example is provided to show the applicability and the performance of our results.

[1]  Kyung-Soo Kim,et al.  Reduced order disturbance observer for discrete-time linear systems , 2013, Autom..

[2]  Myung Jin Chung,et al.  Observer-based H∞ controller design for state delayed linear systems , 1996, Autom..

[3]  Roberto Sanchis,et al.  H∞ Observer Design for a Class of Nonlinear Discrete Systems , 2009, Eur. J. Control.

[4]  R. W. Wilde,et al.  Observers for linear systems with unknown inputs , 1988 .

[5]  Chang-Hua Lien,et al.  New delay-dependent non-fragile H , 2008, Inf. Sci..

[6]  H. Unbehauen,et al.  Communique Robust H = observer design of linear state delayed systems with parametric uncertainty : the discrete-time case 1 , 1999 .

[7]  Roberto Sanchis,et al.  Observer Design for a Class of Nonlinear Discrete Systems. , 2009 .

[8]  Karolos M. Grigoriadis,et al.  A Unified Algebraic Approach To Control Design , 1997 .

[9]  Bahram Shafai,et al.  LTR DESIGN OF PROPORTIONAL-INTEGRAL OBSERVERS , 1995 .

[10]  M. Darouach,et al.  UNKNOWN INPUTS OBSERVERS DESIGN FOR DELAY SYSTEMS , 2007 .

[11]  Mohamed Darouach.  Complements to full order observer design for linear systems with unknown inputs , 2009, Appl. Math. Lett..

[12]  Mohamed Darouach,et al.  H∞ observers design for a class of nonlinear singular systems , 2011, Autom..

[13]  Hyungbo Shim,et al.  An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer , 2009, Autom..

[14]  D. Luenberger.  An introduction to observers , 1971 .

[15]  N. Manamanni,et al.  Design of a robust fault detection based observer for linear switched systems with external disturbances , 2011 .

[16]  Bahram Shafai,et al.  Robust control system design with proportional integral observer , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[17]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[18]  M. Hou,et al.  Design of observers for linear systems with unknown inputs , 1992 .

[19]  Heinz Unbehauen,et al.  Robust Hinfinity observer design of linear state delayed systems with parametric uncertainty: the discrete-time case , 1999, Autom..

[20]  O. Sename,et al.  Unknown inputs proportional integral observers for descriptor systems with multiple delays and unknown inputs , 2004, Proceedings of the 2004 American Control Conference.

[21]  Driss Boutat,et al.  Observers design for a class of nonlinear singular systems , 2011, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[23]  P. Müller,et al.  State estimation of dynamical systems with nonlinearities by using proportional-integral observer , 1995 .

[24]  Jenq-Der Chen.  Robust H∞ output dynamic observer-based control of uncertain time-delay systems , 2007 .

[25]  Dong Ryeol Shin,et al.  Dynamic observers for linear time-invariant systems , 2002, Autom..

[26]  F. Zhu.  Full-order and reduced-order observer-based synchronization for chaotic systems with unknown disturbances and parameters☆ , 2008 .