Stabilization and positivity of 2D fractional order uncertain discrete-time systems

This paper considers the problems of robust stability and stabilization for a class of 2D fractional-order linear time-invariant systems described by the Roesser model with convex polytopic uncertainties. Necessary and sufficient conditions for the positivity and the stabilization by state-feedback control of the problem are established, and an illustrative example is provided to show the usefulness of the proposed results.

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

[2]  Tamal Bose,et al.  Stability of 2-D periodically shift variant filters , 2002 .

[3]  Wu-Sheng Lu,et al.  Some new results on stability and stability robustness of Fornasini-Marchesini state-space 2-D digital filters , 1994, Proceedings of SOUTHEASTCON '94.

[4]  T. Kaczorek Positive 1D and 2D Systems , 2001 .

[5]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[6]  Tadeusz Kaczorek Reachability and controllability to zero of positive fractional discrete-time systems , 2007, 2007 European Control Conference (ECC).

[7]  T. Kaczorek Positivity and stabilization of fractional 2D Roesser model by state-feedbacks, LMI approach , 2009 .

[8]  Tadeusz Kaczorek,et al.  LMI approach to stability of 2D positive systems , 2009, Multidimens. Syst. Signal Process..

[9]  Tadeusz Kaczorek,et al.  Fractional 2D linear systems , 2008 .

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

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

[12]  D. Matignon Stability results for fractional differential equations with applications to control processing , 1996 .

[13]  Haranath Kar,et al.  LMI-based criterion for the robust guaranteed cost control of 2-D systems described by the Fornasini-Marchesini second model , 2007, Signal Process..

[14]  T. Kaczorek,et al.  Positivity and stabilization of fractional 2D linear systems described by the Roesser model , 2009 .

[15]  F. Mainardi Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena , 1996 .

[16]  Zhao Ling-Dong,et al.  A novel stablility theorem for fractional systems and its applying in synchronizing fractional chaotic system based on back-stepping approach , 2009 .

[17]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[18]  Xiaohui Liu,et al.  Robust stability of two-dimensional uncertain discrete systems , 2003, IEEE Signal Process. Lett..

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

[20]  Tadeusz Kaczorek Positive different orders fractional 2D linear systems , 2008 .

[21]  Tyrone Fernando,et al.  Lower bounds for stability margin of two-dimensional discrete systems using the MacLaurine Series , 1999 .

[22]  Tadeusz Kaczorek,et al.  Practical stability and asymptotic stability of positive fractional 2D linear systems , 2010 .

[23]  R. Feynman,et al.  RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING , 2003 .

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

[25]  Maria Elena Valcher,et al.  On the internal stability and asymptotic behavior of 2-D positive systems , 1997 .