Abstract
Robust design techniques are essential in any field of engineering design because the working and durability of their pieces of work is always jeopardized by mutable and unpredictable environments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Machado, J.T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1140–1153 (2011)
Li, C., Zhang, F.: A survey on the stability of fractional differential equations. Eur. Phys. J. Spec. Top. 193(1), 27–47 (2011)
Ortigueira, M.D.: An introduction to the fractional continuous-time linear systems: the 21st century systems. IEEE Circuits Syst. Mag. 8(3), 19–26 (2008)
Xue, D., Chen, Y.: A comparative introduction of four fractional order controllers. In: Intelligent Control and Automation, 2002. Proceedings of the 4th World Congress on, vol. 4, pp. 3228–3235 (2002)
Agrawal, O.P.: A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 38(1–4), 323–337 (2004)
Oustaloup, A., Mathieu, B., Lanusse, P.: The crone control of resonant plants: application to a flexible transmission. Eur. J. Control 1(2), 113–121 (1995)
Podlubny, I.: Fractional-order systems and pi/sup/spl lambda//d/sup/spl mu//-controllers. IEEE Trans. Autom. Control 44(1), 208–214 (1999)
Bouafoura, M.K., Braiek, N.B.: Pi\(\lambda \)d\(\mu \) controller design for integer and fractional plants using piecewise orthogonal functions. Commun. Nonlinear Sci. Numer. Simul. 15(5), 1267–1278 (2010)
Raynaud, H.F., Zergaınoh, A.: State-space representation for fractional order controllers. Automatica 36(7), 1017–1021 (2000)
Utkin, V., Guldner, J., Shi, J.: Sliding mode control in electro-mechanical systems. CRC Press, Boca Raton (2009)
Edwards, C., Spurgeon, S.K.: Sliding mode control: theory and applications. CRC Press, Boca Raton (1998)
Utkin, V.I.: Sliding modes in control and optimization, vol. 116. Springer, Berlin (1992)
Fridman, L., Levant, A.: Higher order sliding modes. Sliding Mode Control Eng. 11, 53–102 (2002)
Si-Ammour, A., Djennoune, S., Bettayeb, M.: A sliding mode control for linear fractional systems with input and state delays. Commun. Nonlinear Sci. Numer. Simul. 14(5), 2310–2318 (2009)
Efe, M.Ö.: Fractional order sliding mode controller design for fractional order dynamic systems. In: New Trends in Nanotechnology and Fractional Calculus Applications, pp. 463–470. Springer (2010)
RamÃrez, H.S., Battle, V.F.: A generalized PI sliding mode and PWM control of switched fractional systems. In: Bartolini, G. et al. (eds.) Modern Sliding Mode Control Theory, LNCIS, vol. 375, pp. 201–221. Springer (2008)
Pisano, A., Rapaić, M., Usai, E.: Second-order sliding mode approaches to control and estimation for fractional order dynamics. In: Fridman, L. et al. (eds.) Sliding Modes after the First Decade of the 21st Century, LNCIS, vol. 412, pp. 169–197. Springer (2012)
Cortes, J.: Discontinuous dynamical systems. IEEE Control Syst. Mag. 28(3), 36–73 (2008)
Filippov, A.F.: Differential equations with discontinuous right-hand side. Matematicheskii sbornik 93(1), 99–128 (1960)
Dieci, L., Lopez, L.: Sliding motion in filippov differential systems: theoretical results and a computational approach. Numer. Anal. 47(3), 2023–2051 (2009)
Danca, M.F.: Approach of a class of discontinuous dynamical systems of fractional order: Existence of solutions. Int. J. Bifurcat. Chaos 21(11), 3273–3276 (2011)
Cernea, A.: Continuous version of filippov’s theorem for fractional differential inclusions. Nonlinear Anal. Theor Methods Appl. 72(1), 204–208 (2010)
Danca, M.F.: Numerical approximation of a class of discontinuous systems of fractional order. Nonlinear Dyn. 66(1–2), 133–139 (2011)
Aubin, J.P., Cellina, A.: Differential inclusions: Set-valued maps and viability theory. Springer, New York (1984)
Sabatier, J., Moze, M., Farges, C.: Lmi stability conditions for fractional order systems. Comput. Math. Appl. 59(5), 1594–1609 (2010)
Petráš, I.: Stability of fractional-order systems with rational orders: a survey. Fractional Calc. Appl. Anal. 12(3), 269–298 (2009)
Ahn, H.S., Chen, Y.: Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica 44(11), 2985–2988 (2008)
Gutman, S., Jury, E.: A general theory for matrix root-clustering in subregions of the complex plane. IEEE Trans. Autom. Control 26(4), 853–863 (1981)
Matignon, D., D’Andrea-Novel, B.: Some results on controllability and observability of finite-dimensional fractional differential systems. In: Computational Engineering in Systems Applications, vol. 2, pp. 952–956. Citeseer (1996)
Senejohnny, D.M., Delavari, H.: Active sliding observer scheme based fractional chaos synchronization. Commun. Nonlinear Sci. Numer. Simul. 17(11), 4373–4383 (2012)
Efe, M.Ö.: Fractional order systems in industrial automation-a survey. IEEE Trans. Industr. Inf. 7(4), 582–591 (2011)
Chen, Y.Q., Petras, I., Xue, D.: Fractional order control-a tutorial. In: American Control Conference, 2009. ACC’09, pp. 1397–1411 (2009)
Andrzej, D., Wiktor, M.: Point to point control of fractional differential linear control systems. Advances in Difference Equations 2011
Anatoly, A.K., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Kamal, S., Raman, A., Bandyopadhyay, B.: Finite time stabilization of fractional order uncertain chain of integrator: a sliding mode approach. In: Industrial Technology (ICIT), 2012 IEEE International Conference on, pp. 1132–1135 (2012)
Miller, K.S., Ross, B.: An Introduction to The Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, INC (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bandyopadhyay, B., Kamal, S. (2015). Sliding Mode Control of Fractional Order Systems. In: Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach. Lecture Notes in Electrical Engineering, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-319-08621-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-08621-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08620-0
Online ISBN: 978-3-319-08621-7
eBook Packages: EngineeringEngineering (R0)