Page 170 - Mathematical Techniques of Fractional Order Systems

158 Mathematical Techniques of Fractional Order Systems

Matignon, D., 1998. Generalized fractional differential and difference equations: stability proper-
ties and modelling issues, in: Proc. Mathematical Theory of Networks and Systems
Symposium, Padova, Italy. pp. 503 506.
Matsuda, K., Fuji, H., 1993. H N optimized wave-absorbing control: analytical and experimental
results. J. Guidance, Contr. Dynamics 16, 1146 1153.
Mihailo, P.L., Aleksandar, M.S., 2009. Finite-time stability analysis of fractional order time-
delay systems: Gronwall’s approach. Math. Computer Modelling 49, 475 481.
Montseny, G., 1998. Diffusive representation of pseudo-differential time-operators, in: ESAIM:
Proceedings, Fractional Differential Systems: Models, Methods and Applications, EDP
Sciences, pp. 159 175.
Ortigueira, M.D., Machado, J.A.T., 2003. Editorial: fractional signal processing and applications.
Signal Process. 83, 2285 2286.
Oustaloup, A., 1991. La Commande CRONE. Hermes, Paris.
Oustaloup, A., 1995. La De ´rivation Non Entie `re: Synthe ´se et Applications. Hermes, Paris.
Podlubny, I., 1999. Fractional Differential Equations. Academic, New York.
Podlubny, I., 2002. Geometric and physical interpretation of fractional integration and fractional
differentiation. Fract. Calculus Appl. Anal. 5, 367 386.
Sabatier, J., Agrawal, O.P., Machado, J.A.T., 2007. Advances in Fractional Calculus: Theoretical
Developments and Applications in Physics and Engineering. Springer, New York.
Sabatier, J., Merveillaut, M., Malti, R., Oustaloup, A., 2010. How to impose physically coherent
initial conditions to a fractional system? Commun Nonlinear Sci. Numer. Simulat. 10,
1318 1326.
Sabatier, J., Farges, C., Trigeassou, J., 2014. Fractional systems state space description: some
wrong ideas and proposed solutions. J. Vibration Control 20, 1076 1084.
Sheng, H., Chen, Y., Qiu, T., 2012. Fractional Processes and Fractional-Order Signal Processing
- Techniques and Applications. Springer, Berlin.
Si-Ammour, A., Djennoune, S., Bettayeb, M., 2009. A sliding mode control for linear fractional
systems with input and state delays. Commun. Nonlinear Sci. Numer. Simul. 14,
2310 2318.
Sierociuk, D., Dzieli´ nski, A., Sarwas, G., Petras, I., Podlubny, I., Skovranek, T., 2013. Modelling
heat transfer in heterogeneous media using fractional calculus. Philos. Trans. R. Soc., A 371.
Tarbouriech, S., 1997. Local stabilization of continuous-time delay systems with bounded inputs,
in: Proc. European Contr. Conf., Brussels, Belgium. pp. 3684 3689.
Trigeassou, J., Maamri, N., Sabatier, J., Oustaloup, A., 2011. A Lyapunov approach to the stabil-
ity of fractional differential equations. Signal Process. 91, 437 445.
Trigeassou, J.C., Maamri, N., 2009. State space modeling of fractional differential equations and
the initial condition problem, in: Systems, Signals and Devices, 2009. SSD ’09. 6th
International Multi-Conference on, pp. 1 7.
Vinagre, B., 2001. Modeling and Control of Dynamic Systems characterized by Integro-
differential Equations of Fractional Order. Ph.D. thesis. University of Distance Education.
Spain.
Vinagre, B.M., Podlubny, I., Herna ´ndez, A., Feliu, V., 2000. Some Approximations of fractional
order operators used in control theory and applications. Fract. Calculus Appl. Anal. 3,
231 248. chapter 3.
Yuan, L., Yang, Q., Zeng, C., 2013. Chaos detection and parameter identification in fractional-
order chaotic systems with delay. Nonlinear Dynam. 73, 439 448.