### Details

#### 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#### Numer

No 2#### Publication authors

#### Divisions of PAS

Nauki Techniczne#### Coverage

195-200#### Publisher

Polish Academy of Sciences#### Date

2011#### Identifier

ISSN 0239-7528, eISSN 2300-1917#### 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#### DOI

10.2478/v10175-011-0024-z