Observer design for unknown input nonlinear descriptor systems via convex optimization

This paper treats the design problem of full-order observers for nonlinear descriptor systems with unknown input (UI). Depending on the available knowledge on the UI dynamics, two cases are considered. First, a UI proportional observer (UIPO) is proposed when the spectral domain of the UI is unknown. Second, a PIO is proposed when the spectral domain of the UI is in the low frequency range. Sufficient conditions for the existence and stability of such observers are given and proved. Based on the linear matrix inequality (LMI) approach, an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective. An example is included to illustrate the method.

[1]  P. Kaboré,et al.  Disturbance attenuation using proportional integral observers , 2001 .

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

[3]  D. N. Shields.  Observer design and detection for nonlinear descriptor systems , 1997 .

[4]  G. Zimmer,et al.  On observ-ing nonlinear descriptor systems , 1997 .

[5]  Didier Georges,et al.  Robust fault diagnosis for linear descriptor systems using proportional integral observers , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[6]  J. Hedrick,et al.  Observer design for a class of nonlinear systems , 1994 .

[7]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[8]  S. P. Linder,et al.  Proportional integral adaptive observer for parameter and disturbance estimations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Janos Turi,et al.  An observer for a nonlinear descriptor system , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[10]  R. Rajamani,et al.  A systematic approach to adaptive observer synthesis for nonlinear systems , 1997, IEEE Trans. Autom. Control..

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

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

[13]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[14]  F. Thau.  Observing the state of non-linear dynamic systems† , 1973 .

[15]  M. Boutayeb,et al.  Observers design for nonlinear descriptor systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[16]  Saïd Mammar,et al.  Design of proportional-integral observer for unknown input descriptor systems , 2002, IEEE Trans. Autom. Control..

[17]  M. Darouach,et al.  Reduced-order observer design for descriptor systems with unknown inputs , 1996, IEEE Trans. Autom. Control..

[18]  G. Sallet,et al.  Observers for Lipschitz non-linear systems , 2002 .

[19]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[20]  Zhengzhi Han,et al.  A note on observers for Lipschitz nonlinear systems , 2002, IEEE Trans. Autom. Control..

[21]  Dirk van Schrick,et al.  Some aspects on the proportional-integral observer in the field of system supervision , 1999 .

[22]  K. S. Banerjee.  Generalized Inverse of Matrices and Its Applications , 1973 .

[23]  Antonio Tornambè,et al.  Asymptotic observers for non-linear systems , 1992 .

[24]  Wei-bing Gao,et al.  On exponential observers for nonlinear systems , 1988 .

[25]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[26]  Sun Liying,et al.  State and input estimation for descriptor systems with unknown inputs , 2004, Proceedings of the 2004 American Control Conference.

[27]  B. Shafai,et al.  Robust control system design with a proportional integral observer , 1989 .

[28]  C. R. Rao,et al.  Generalized Inverse of Matrices and its Applications , 1972 .