Analysis and design of unknown input observers for a class of 2-D nonlinear systems

This paper considers the analysis and design of asymptotic unknown input observers (UIOs) for a class of two-dimensional (2-D) nonlinear systems. A sufficient condition for the existence of an asymptotic UIO such that the observer estimation error asymptotically converges to zero is first given in terms of a rank condition on the given system matrices. A systematic method is then presented for the design of UIOs using a linear matrix inequality technique. An example is provided to illustrate the effectiveness of the proposed design method.

[1]  Zhiping Lin,et al.  The existence and design of functional observers for two-dimensional systems , 2012, Syst. Control. Lett..

[2]  Lorenzo Ntogramatzidis,et al.  Detectability subspaces and observer synthesis for two-dimensional systems , 2012, Multidimens. Syst. Signal Process..

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

[4]  Maria Elena Valcher,et al.  The general fault detection and isolation problem for 2D state-space models , 2006, Syst. Control. Lett..

[5]  A. Michel,et al.  Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities , 1994 .

[6]  Zhiping Lin,et al.  A New Constructive Procedure for 2-D Coprime Realization in Fornasini–Marchesini Model , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Truong Q. Nguyen,et al.  Robust mixed generalized H/sub 2//H/sub /spl infin// filtering of 2-D nonlinear fractional transformation systems , 2005, IEEE Transactions on Signal Processing.

[8]  Lorenzo Ntogramatzidis,et al.  A geometric theory for 2-D systems including notions of stabilisability , 2008, Multidimens. Syst. Signal Process..

[9]  Cishen Zhang,et al.  H∞ and Robust Control of 2-D Systems in FM Second Model , 2002, Multidimens. Syst. Signal Process..

[10]  Vimal Singh,et al.  Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  J. E. Kurek,et al.  Stability of nonlinear parameter-varying digital 2-D systems , 1995, IEEE Trans. Autom. Control..

[12]  Shengyuan Xu,et al.  Analysis and control of the jump modes behavior of 2-D singular systems - Part II: Regular observer and compensator design , 2007, Syst. Control. Lett..

[13]  Zhiping Lin,et al.  Coefficient-dependent direct-construction approach to realization of multidimensional systems in Roesser model , 2011, Multidimens. Syst. Signal Process..

[14]  M. Bisiacco On the structure of 2-D observers , 1986 .

[15]  Vimal Singh,et al.  Stability Analysis of 2-D Discrete Systems Described by the Fornasini–Marchesini Second Model With State Saturation , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[17]  T. Kaczorek Two-Dimensional Linear Systems , 1985 .

[18]  Derong Liu,et al.  Lyapunov stability of two-dimensional digital filters with overflow nonlinearities , 1998 .

[19]  K. Galkowski,et al.  Positive real control for uncertain two-dimensional systems , 2002 .

[20]  Weiqun Wang,et al.  The detectability and observer design of 2-D singular systems , 2002 .

[21]  Leonard T. Bruton,et al.  BIBO stability of inverse 2-D digital filters in the presence of nonessential singularities of the second kind , 1989 .

[22]  Li Xu,et al.  $${{\mathcal H}_{\infty}}$$ control of linear multidimensional discrete systems , 2012, Multidimens. Syst. Signal Process..

[23]  Zhiping Lin,et al.  Asymptotic unknown input observers for two-dimensional systems , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[24]  Mauro Bisiacco,et al.  Unknown input observers for 2D state-space models , 2004 .

[25]  T. Ooba On stability analysis of 2-D systems based on 2-D Lyapunov matrix inequalities , 2000 .