Antsaklis P.J. and Michel A.N. (1997). *Linear Systems*, McGraw-Hill, New York.

Åström K. J. and Wittenmark B. (1996). *Computer- Controlled Systems, Theory and Design, 3rd Ed.*, Prentice Hall Inc., New Jersey.

Axtell M. and Bise E. M. (1990). Fractional calculus applications in control systems, *Proceedings of the IEEE 1990 National Aerospace and Electronics Conference, New York, USA*, pp. 536-566.

Battaglia J. L., Cois O., Puigsegur L. and Oustaloup A. (2001). Solving an inverse heat conduction problem using a non-integer identified model, *International Journal of Heat and Mass Transfer*, 44(14): 2671-2680.

Bettayeb M. and Djennoune S. (2006). A note on the controllability and the observability of fractional dynamical systems, *Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Workshop Applications, Porto, Portugal*, pp. 506-511.

Boukas E.K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability, *Mathematical Problems in Engineering*, bf 2006 (ID42489): 1-10.

Cois O., Oustaloup A., Battaglia E. and Battaglia J.L. (2002). Non integer model from modal decomposition for time domain identification, *41st IEEE CDC'2002 Tutorial Workshop 2, Las Vegas, USA.*

Debeljković D. Lj., Aleksendrić M., Yi-Yong N. and Zhang Q. L. (2002). Lyapunov and non-Lyapunov stability of linear discrete time delay systems, *Facta Universitatis, Series: Mechanical Engineering* 1(9): 1147-1160.

Dorĉák L., Petras I. and Kostial I. (2000). Modeling and analysis of fractional-order regulated systems in the state-space, *Procedings of International Carpathian Control Conference, High Tatras, Slovak Republic*, pp. 185-188.

Dzieliński A. and Sierociuk D. (2005). Adaptive feedback control of fractional order discrete state-space systems, *Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation, and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'05), Vienna Austria*, pp. 804-809.

Dzieliński A. and Sierociuk D. (2006). Observer for discrete fractional order systems, *Proceedings of the 2nd IFAC Workshop on Fractional Differentiation Applications, Porto, Portugal*, pp. 524-529.

Dzieliński A. and Sierociuk D. (2007). Reachability, controllability and observability of the fractional order discrete statespace system, *Proceedings of the IEEE/IFAC International Conference on Methods and Models in Automation and Robotics, MMAR'2007, Szczecin, Poland*, pp. 129-134.

Gorenflo R. and Mainardi F. (1997). Fractional calculus: Integral and differential equations of fractional order, *in* (A. Carpintieri and F. Mainardi, Eds.) *Fractals and Fractional Calculus in Continuum Mechanics*, Vienna, New York, Springer Verlag.

Hanyga A. (2003). Internal variable models of viscoelasticity with fractional relaxation laws, *Proceddings of Design Engineering Technical Conference, Mechanical Vibration and Noise, 48395, American Society of Mechanical Engineers, Chicago, USA.*

Hotzel R. and Fliess M. (1998). On linear system with a fractional derivation: Introductory theory and examples, *Mathematics and Computers in Simulation* 45(3): 385-395.

Ichise M., Nagayanagi Y. and Kojima T. (1971). An analog simulation of non integer order transfer functions for analysis of electrode processes, *Journal of Electroanalytical Chemistry* 33(2): 253-265. [Crossref]

Kilbas A. A., Srivasta H.M. and Trujillo J. J. (2006). *Theory and Applications of Fractional Differential Equations*, Elsevier, Amsterdam.

Lakshmikantham D. T. V. (1998). *Theory of Difference Equations: Numerical Methods and Applications*, Academic Press, New York.

Manabe S. (1960). The non-integer integral and its application to control systems, *Japanese Institute of Electrical Engineers Journal* 80(860): 589-597.

Matignon D. (1994). *Reprèsentation en variables d'ètat de modèles de guides d'ondes avec dèrivation fractionnaire*, Ph.D. thesis, Universitè Paris XI, France.

Matignon D., d'Andrèa Novel B., Depalle P. and Oustaloup A. (1994). *Viscothermal Losses in Wind Instruments: A Non-Integer Model*, Academic Verlag, Berlin.

Matignon D. and d'Andrèa-Novel B. (1996). Some results on controllability and observability of finite-dimensional fractional differential systems, *Proceedings of the IMACS, IEEE SMC Conference, Lille, France*, pp. 952-956.

Matignon D. (1996). Stability results on fractional differential with application to control processing, *Proceedings of the IAMCS, IEEE SMC Conference, Lille, France*, pp. 963-968.

Miller K. S. and Ross B. (1993). *An Introduction to the Fractional Calculus and Fractional Differential Equations*,Wiley, New York.

Mittag-Leffler G. (1904). Sur la reprèsentation analytique d'une branche uniforme d'une fonction monogène, *Acta Mathematica* 29: 10-181.

Oldham K. B. and Spanier J. (1974). *The Fractional Calculus*, Academic Press, New York.

Oustaloup A. (1983). *Systèmes asservis linèaires d'ordre fractionnaire*, Masson, Paris.

Oustaloup A. (1995). *La Dèrivation non entière: Thèorie, synthèse et applications*, Hermès, Paris.

Peng Y., Guangming X. and Long W. (2003). *Controllability of linear discrete-time systems with time-delay in state*, available at http://dean.pku.edu.cn/bksky/1999tzlwj/4.pdf

Podlubny I. (1999). *Fractional Differential Equations*, Academic Press, San Diego.

Raynaud H. F., Zergainoh A. (2000). State-space representation for fractional-order controllers, *Automatica* 36(7): 1017-1021. [Crossref]

Sabatier J., Cois O. and Oustaloup A. (2002). Commande de systèmes non entiers par placement de pôles, *Deuxième Confèrence Internationale Francophone d'Automatique, CIFA, Nantes, France.*

Samko S. G., Kilbas A. A. and Marichev O. I. (1993). *Fractional Integrals and Derivatives: Theory and Applications*, Gordon and Breach, Amsterdam.

Sierociuk D. and Dzieliński A. (2006). Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, *International Journal of Applied Mathematics and Computer Science* 16(1): 129-140.

Valerio D. and Sa da Costa J. (2004). Non-integer order control of a flexible robot, *Proceedings of the IFAC Workshop on Fractional Differentiation and its Applications, FDA'04, Bordeaux, France.*

Vinagre B. M., Monje C. A. and Caldero A. J. (2002). Fractional order systems and fractional order actions, *Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics, 41st IEEE CDC, Las Vegas, USA.*

## Comments (0)