Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems

Bulletin of the Polish Academy of Sciences: Technical Sciences

Volumn 61, Issue 2, 2013, Pages 363-370

  Stanislawski R ^a   Latawiec, K J ^a  

^a OPOLE UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

closed loop stability; discrete time fractional order systems; Gr nwald Letnikov fractional difference; nonminimum phase system; stability criterion

Indexed keywords

CLOSED LOOP STABILITY; CLOSED-LOOP STABILITY ANALYSIS; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; NECESSARY AND SUFFICIENT STABILITY CONDITIONS; NON-MINIMUM PHASE SYSTEMS; STABILITY ANALYSIS; STATE SPACE SYSTEMS;

ASYMPTOTIC STABILITY; STABILITY CRITERIA;

FINITE DIFFERENCE METHOD;

EID: 84883475500     PISSN: 02397528     EISSN: None     Source Type: Journal    
DOI: 10.2478/bpasts-2013-0035     Document Type: Article

References (15)

1. M. Busłowicz, "Robust stability of positive discrete-time linear systems of fractional order", Bull. Pol. Ac. Tech. 58 (4), 567-572 (2010
2. M. Busłowicz and T. Kaczorek, "Simple conditions for practical stability of positive fractional discrete-time linear systems", Int. J. Applied Mathematics and Computer Science 19 (2), 263-269 (2009
3. T. Kaczorek, "Practical stability of positive fractional discretetime linear systems", Bull. Pol. Ac. Tech. 56 (4), 313-317 (2008
4. T. Kaczorek, "New stability tests of positive standard and fractional linear systems", Circuits and Systems, 2 (4), 261-268 (2011
5. T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011
6. S. Guermah, S. Djennoune, and M. Bettayeb, "A new approach for stability analysis of linear discrete-time fractional-order systems", in New Trends in Nanotechnology and Fractional Calculus Applications, eds. D. Baleanu, Z.B. Güvenç, and J.A.T. Machado, pp. 151-162, Springer, Dordrecht, 2010
7. S.B. Stojanovic and D.L. Debeljkovic, "Simple stability conditions of linear discrete time systems with multiple delay", Serbian J. Electrical Engineering 7 (1), 69-79 (2010
8. D. Matignon, "Stability results for fractional differential equations with applications to control processing", Computational Engineering in Systems Applications 2, 963-968 (1996
9. D. Matignon, "Stability properties for generalized fractional differential systems", ESAIM: Proc. 5, 145-158 (1998
10. R. Stanisławski and K.J. Latawiec, "Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability", Bull. Pol. Ac. Tech. 61 (2), 353-361 (2013
11. A. Dzieliński and D. Sierociuk, "Stability of discrete fractional order state-space systems", J. Vibration and Control 14 (9-10), 1543-1556 (2008
12. C. Monje, Y. Chen, B. Vinagre, D. Xue, and V. Feliu, Fractional-order Systems and Controls, Springer-Verlag, London, 2010
13. R. Stanisławski and K.J. Latawiec, "Normalized finite fractional differences -the computational and accuracy breakthroughs", Int. J. Applied Mathematics and Computer Science 22 (4), 907-919 (2012
14. W.P. Hunek and K.J. Latawiec, "A study on new right/left inverses of nonsquare polynomial matrices", Int. J. Applied Mathematics and Computer Science 21 (2), 331-348 (2011
15. K.J. Latawiec, The Power of Inverse Systems in Linear and Nonlinear Modeling and Control, Opole University of Technology Press, Opole, 2004