On the stability of 2D state-space models

In this paper, we consider the problem of stability of two-dimensional linear systems. New sufficient conditions for the asymptotic stability are derived in terms of linear matrix inequalities.

[1]  Yurii Nesterov,et al.  Positivity and Linear Matrix Inequalities , 2002, Eur. J. Control.

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

[3]  T. Kaczorek.  The singular general model of 2D systems and its solution , 1988 .

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

[5]  D. Davis,et al.  A correct proof of Huang's theorem on stability , 1976 .

[6]  Paul Van Dooren,et al.  Optimization Problems over Positive Pseudopolynomial Matrices , 2003, SIAM J. Matrix Anal. Appl..

[7]  D. Siljak.  Stability criteria for two-variable polynomials , 1975 .

[8]  Thomas S. Huang,et al.  Stability of two-dimensional recursive filters , 1972 .

[9]  G. Marchesini,et al.  Stability analysis of 2-D systems , 1980 .

[10]  J. Kurek,et al.  The general state-space model for a two-dimensional linear digital system , 1985 .

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

[12]  H. Ansell.  On Certain Two-Variable Generalizations of Circuit Theory, with Applications to Networks of Transmission Lines and Lumped Reactances , 1964 .

[13]  J. Murray.  Another proof and a sharpening of Huang's theorem , 1977 .

[14]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[15]  Yun Zou,et al.  Stability for two-dimensional singular discrete systems described by general model , 2008, Multidimens. Syst. Signal Process..

[16]  T. Kaczorek.  Stabilization of singular 2-D continuous-discrete systems by state-feedback controllers , 1996, IEEE Trans. Autom. Control..

[17]  E. Rogers,et al.  Positive real control of two-dimensional systems: Roesser models and linear repetitive processes , 2003 .