Nonlinear Dynamics

, Volume 85, Issue 1, pp 167–177 | Cite as

Asymptotic stability and stabilization of a class of nonautonomous fractional order systems

  • Bichitra Kumar Lenka
  • Soumitro Banerjee
Original Paper


Many physical systems from diverse fields of science and engineering are known to give rise to fractional order differential equations. In order to control such systems at an equilibrium point, one needs to know the conditions for stability. In this paper, the conditions for asymptotic stability of a class of nonautonomous fractional order systems with Caputo derivative are discussed. We use the Laplace transform, Mittag–Leffler function and generalized Gronwall inequality to derive the stability conditions. At first, new sufficient conditions for the local and global asymptotic stability of a class of nonautonomous fractional order systems of order \(\alpha \) where \(1<\alpha <2\) are derived. Then, sufficient conditions for the local and global stabilization of such systems are proposed. Using the results of these theorems, we demonstrate the stabilization of some fractional order nonautonomous systems which illustrate the validity and effectiveness of the proposed method.


Nonautonomous fractional order systems Asymptotic stability Mittag–Leffler function Generalized Gronwall inequality  Stabilization Linear feedback control 



The author Bichitra Kumar Lenka sincerely acknowledges the University Grants Commission, India, under Grant No. F. 2-6/2008 (SA-I) for financial support.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Science Education and Research KolkataMohanpur CampusIndia
  2. 2.Department of Physical SciencesIndian Institute of Science Education and Research KolkataMohanpur CampusIndia

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