Details Details PDF BIBTEX RIS Title Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model Journal title Bulletin of the Polish Academy of Sciences Technical Sciences Yearbook 2011 Volume 59 Issue No 2 Authors Rogowski, K. Divisions of PAS Nauki Techniczne Coverage 195-200 Date 2011 Identifier DOI: 10.2478/v10175-011-0024-z ; ISSN 2300-1917 Source Bulletin of the Polish Academy of Sciences: Technical Sciences; 2011; 59; No 2; 195-200 References Roesser R. (1975), A discrete state-space model for linear image processing, IEEE Trans. Autom. Contr, AC-20, 1, 1, doi.org/10.1109/TAC.1975.1100844 ; Fornasini E. (1976), State-space realization theory of two-dimensional filters, IEEE Trans. Autom. Contr, AC-21, 484, doi.org/10.1109/TAC.1976.1101305 ; Fornasini E. (1978), Double indexed dynamical systems, Math. Syst. Theory, 12, 59. ; Kurek J. (1985), The general state-space model for a two-dimensional linear digital systems, IEEE Trans. Autom. Contr, AC-30, 600, doi.org/10.1109/TAC.1985.1103998 ; Kaczorek T. (1996), Reachability and controllability of non-negative 2D Roesser type models, Bull. Pol. Ac.: Tech, 44, 4, 405. ; Kaczorek T. (2001), Positive 1D and 2D Systems. ; Kaczorek T. (2005), Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics, 34, 2, 411. ; Valcher M. (1997), On the internal stability and asymptotic behavior of 2D positive systems, IEEE Trans. on Circuits and Systems - I, 44, 7, 602, doi.org/10.1109/81.596941 ; Bose N. (1982), Applied Multidimensional Systems Theory. ; Bose N. (1985), Multidimensional Systems Theory Progress, Directions and Open Problems. ; Galkowski K. (2001), State Space Realizations of Linear 2D Systems with Extensions to the General nD (n > 2) Case. ; Kaczorek T. (1985), Two-Dimensional Linear Systems. ; Farina E. (2000), Positive Linear Systems: Theory and Applications. ; Kaczorek T. (2008), Asymptotic stability of positive 1D and 2D linear systems, Recent Advances in Control and Automation, 1, 41. ; Kaczorek T. (2008), Asymptotic stability of positive 2D linear systems, null, 1. ; Kaczorek T. (2009), LMI approach to stability of 2D positive systems, Multidimensional Systems and Signal Processing, 20, 1, 39, doi.org/10.1007/s11045-008-0050-7 ; Twardy M. (2007), An LMI approach to checking stability of 2D positive systems, Bull. Pol. Ac.: Tech, 55, 4, 385. ; Kaczorek T. (2009), Positivity and stabilization of 2D linear systems, Discuss. Math. Differ. Inclusions, 29, 43. ; Miller K. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations. ; Nashimoto K. (1984), Fractional Calculus. ; Oldham K. (1974), The Fractional Calculus. ; Podlubny I. (1999), Fractional Differential Equations. ; Ostalczyk P. (2008), Epitome of Fractional Calculus, Theory and its Applications in Automatics. ; Kaczorek T. (2008), Fractional 2D linear systems, J. Automation, Mobile Robotics & Intelligent Systems, 2, 2, 5. ; Kaczorek T. (2008), Positive different orders fractional 2D linear systems, Acta Mechanica et Automatica, 2, 2, 51. ; Kaczorek T. (2009), Positive 2D fractional linear systems, COMPEL, 28, 2, 341. ; Kaczorek T. (2009), Positivity and stabilization of fractional 2D Roesser model by state feedbacks, LMI approach, Archives of Control Science, 19, 2, 165. ; Kaczorek T. (2010), Positivity and stabilization of fractional 2D linear systems described by the Roesser model, Int. J. Appl. Math. Comp. Sci, 20, 1, 86. ; Murty M. (2005), Controllability and observability of Lyapunov systems, Ranchi University Mathematical J, 32, 55. ; Kaczorek T. (2007), Positive discrete-time linear Lyapunov systems, null, 1. ; Kaczorek T. (2007), Continuous-time linear Lyapunov cone-systems, Proc. 13<sup>th</sup> IEEE IFAC Int. Conf. Methods and Models in Automation and Robotics, 1, 225. ; Kaczorek T. (2007), Positive continuous-time linear Lyapunov systems, Proc. Int. Conf. Computer as a Tool, EUROCON, 1, 731, doi.org/10.1109/EURCON.2007.4400242 ; Kaczorek T. (2007), Positive continuous-time linear time-varying Lyapunov systems, Proc. 16<sup>th</sup> Int. Conf. Systems Science, 1, 140. ; Kaczorek T. (2009), Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems, Control and Cybernetics, 38, 2, 529. ; Przyborowski P. (2009), Positive discrete-time linear Lyapunov systems, Int. J. Appl. Math. Comp. Sci, 19, 1, 95, doi.org/10.2478/v10006-009-0009-3 ; Przyborowski P. (2008), Positive fractional discrete-time Lyapunov systems, Archives of Control Science, 18, 1, 121. ; Przyborowski P. (2008), Fractional discrete-time Lyapunov cone-systems, Electrotechnical Review, 84, 5, 47. ; Kaczorek T. (1998), Vectors and Matrices in Automation and Electrotechnics. ; Buslowicz M. (2008), Simple stability conditions for linear positive discrete-time systems with delays, Bull. Pol. Ac.: Tech, 56, 4, 325. ; Buslowicz M. (2009), Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comp. Sci, 19, 2, 263, doi.org/10.2478/v10006-009-0022-6 ; Kaczorek T. (2007), Choice of the forms of Lyapunov functions for positive 2D Roesser model, Int. J. Appl. Math. Comp. Sci, 17, 4, 471, doi.org/10.2478/v10006-007-0039-7