### Details

#### Title

Stability and stabilization of positive fractional linear systems by state-feedbacks#### Journal title

Bulletin of the Polish Academy of Sciences: Technical Sciences#### Yearbook

2010#### Volume

58#### Numer

No 4#### Authors

#### Divisions of PAS

Nauki Techniczne#### Coverage

537-554#### Date

2010#### Identifier

ISSN 2300-1917#### References

Farina L. (2000), Positive Linear Systems; Theory and Applications. ; Kaczorek T. (2002), Positive 1D and 2D Systems. ; Kaczorek T. (2007), Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences, 17, 3, 357. ; Kaczorek T. (2006), Computation of realizations of discrete-time cone systems, Bull. Pol. Ac.: Tech, 54, 3, 347. ; Roesser R. (1975), A discrete state-space model for linear image processing, IEEE Trans. Autom. Contr, 20, 1, 1, doi.org/10.1109/TAC.1975.1100844 ; Fornasini E. (1978), Double indexed dynamical systems, Math. Sys. 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. (2005), Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics, 34, 2, 411. ; Kaczorek T. (2006), Positive 2D systems with delays, null. ; Valcher M. (1997), On the internal stability and asymptotic behavior of 2D positive systems, IEEE Trans. on Circuits and Systems, 44, 7, 602. ; Kaczorek T. (2008), Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, J. Automation and System Engineering, 42, 6-8, 769. ; Klamka J. (1991), Controllability of Dynamical Systems. ; Klamka J. (2002), Positive controllability of positive systems, null, 1. ; Busłowicz M. (2008), Simple stability conditions for linear positive discrete-time systems with delays, Bull. Pol. Ac.: Tech, 56, 4, 325. ; Gałkowski K. (2005), Fractional polynomials and <i>n</i>D systems, null, 1. ; Kaczorek T. (2008), Asymptotic stability of positive 1D and 2D linear systems, Recent Advances in Control and Automation, 1, 41. ; 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 ; Kaczorek T. (2009), Asymptotic stability of positive 2D linear systems with delays, Bull. Pol. Ac.: Tech, 57, 2, 133. ; Busłowicz M. (2007), Robust stability of positive discrete-time linear systems with multiple delays with unity rank uncertainty structure or non-negative perturbation matrices, Bull. Pol. Ac.: Tech, 55, 1, 347. ; Miller K. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations. ; Nashimoto K. (1984), Fractional Calculus. ; Oldham K. (1974), The Fractional Calculus. ; Ostalczyk P. (2008), Epitome of the Fractional Calculus, Theory and its Applications in Automatics. ; Oustaloup A. (1993), Commande CRONE. ; Podlubny I. (1999), Fractional Differential Equations. ; Kaczorek T. (2007), Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotics Control, 6, 4, 130. ; Kaczorek T. (2008), Fractional positive continuous-time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci, 18, 2, 223, doi.org/10.2478/v10006-008-0020-0 ; Kaczorek T. (2008), Asymptotic stability of positive 2D linear systems, null. ; Kaczorek T. (2008), Practical stability of positive fractional discretetime linear systems, Bull. Pol. Ac.: Tech, 56, 4, 313. ; Kaczorek T. (2009), Independence of the asymptotic stability of positive the 2D linear systems with delays of their delays, Int. J. Appl. Math. Comput. Sci, 19, 2, 255, doi.org/10.2478/v10006-009-0021-7 ; Twardy M. (2007), An LMI approach to checking stability of 2D positive systems, Bull. Pol. Ac.: Tech, 55, 4, 379. ; 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. ; Ostalczyk P. (2000), The non-integer difference of the discrete-time function and its application to the control system synthesis, Int. J. Syst, Sci, 31, 12, 1551, doi.org/10.1080/00207720050217322 ; Sierociuk D. (2006), Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, Int. J. Appl. Math. Comp. Sci, 16, 1, 129. ; Vinagre M. (2002), Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures, null, 1, 214. ; Kaczorek T. (2009), Positivity and stabilization of fractional 2D linear systems described by Roesser model, null, 1.#### DOI

10.2478/v10175-010-0054-y