Robust stability of 2-D digital filters employing saturation

A computationally tractable, i.e., linear matrix inequality (LMI)-based criterion for the global asymptotic stability of uncertain two-dimensional digital filters described by the Fornasini-Marchesini second local state-space model with saturation overflow arithmetic is presented. The criterion is compared with an earlier LMI-based criterion.

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

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[3]  David J. Hill,et al.  Reply to "Comments on 'stability and absence of over ow oscillations for 2-d discrete-time systems" , 1999, IEEE Trans. Signal Process..

[4]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[5]  Wu-Sheng Lu,et al.  Some new results on stability robustness of two-dimensional discrete systems , 1994, Multidimens. Syst. Signal Process..

[6]  Hj Hans Butterweck,et al.  Finite wordlength effects in digital filters : a review , 1988 .

[7]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[8]  Vimal Singh,et al.  Stability analysis of 2-D state-space digital filters with overflow nonlinearities , 2000 .

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

[10]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[11]  N. El-Agizi,et al.  Two-dimensional digital filters with no overflow oscillations , 1979 .

[12]  Wu-Sheng Lu,et al.  On robust stability of 2-D discrete systems , 1995, IEEE Trans. Autom. Control..

[13]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

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

[15]  Spyros G. Tzafestas,et al.  Two-dimensional digital filters without overflow oscillations and instability due to finite word length , 1992, IEEE Trans. Signal Process..

[16]  Y. Hung,et al.  Robust mixed H/sub 2//H/sub /spl infin// filtering with regional pole assignment for uncertain discrete-time systems , 2002 .

[17]  Vimal Singh,et al.  Stability analysis of 2-D state-space digital filters using Lyapunov function: a caution , 1997, IEEE Trans. Signal Process..

[18]  Vimal Singh.  A new realizability condition for limit cycle-free state-space digital filters employing saturation arithmetic , 1985 .

[19]  Peter H. Bauer,et al.  Comments on "Stability and absence of overflow oscillations for 2-D discrete-time systems" , 1998, IEEE Trans. Signal Process..

[20]  Lihua Xie,et al.  H∞ deconvolution filtering of 2-d digital systems , 2002, IEEE Trans. Signal Process..

[21]  Xinping Guan,et al.  Robust optimal guaranteed cost control for 2D discrete systems , 2001 .

[22]  T. Hinamoto.  Stability of 2-D discrete systems described by the Fornasini-Marchesini second model , 1997 .

[23]  C. Du,et al.  Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach , 1999 .

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

[25]  David J. Hill,et al.  Stability and absence of overflow oscillations for 2-D discrete-time systems , 1996, IEEE Trans. Signal Process..

[26]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[27]  Vimal Singh,et al.  Stability analysis of 2-D digital filters described by the Fornasini-Marchesini second model using overflow nonlinearities , 2001 .

[28]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

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

[30]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[31]  Lihua Xie,et al.  H∞ filtering of 2-D discrete systems , 2000, IEEE Trans. Signal Process..

[32]  Truong Q. Nguyen,et al.  Robust Mixed Filtering of 2-D Systems , 2002 .

[33]  T. Hinamoto.  2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model , 1993 .

[34]  Wu-Sheng Lu.  On a Lyapunov approach to stability analysis of 2-D digital filters , 1994 .

[35]  V. Singh,et al.  Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities , 2001, IEEE Trans. Signal Process..

[36]  T. Claasen,et al.  Effects of quantization and overflow in recursive digital filters , 1976 .

[37]  E. Kaszkurewicz,et al.  Stability of asynchronous two-dimensional Fornasini-Marchesini dynamical systems , 2001 .

[38]  Truong Q. Nguyen,et al.  Robust mixed 𝒽2/𝒽∞ filtering of 2-D systems , 2002, IEEE Trans. Signal Process..