Practical stability analysis of fractional-order impulsive control systems.

In this paper we obtain sufficient conditions for practical stability of a nonlinear system of differential equations of fractional order subject to impulse effects. Our results provide a design method of impulsive control law which practically stabilizes the impulse free fractional-order system.

[1]  V. Lakshmikantham,et al.  Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems , 1991 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  Michal Fečkan,et al.  On the new concept of solutions and existence results for impulsive fractional evolution equations , 2011 .

[4]  Ivanka M. Stamova,et al.  Stability Analysis of Impulsive Functional Differential Equations , 2009 .

[5]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[6]  Bashir Ahmad,et al.  Existence of Solutions for Impulsive Anti-periodic Boundary Value Problems of Fractional Order , 2011 .

[7]  Lansun Chen,et al.  The dynamics of an epidemic model for pest control with impulsive effect , 2010 .

[8]  Liu Jin-Gui,et al.  A novel study on the impulsive synchronization of fractional-order chaotic systems , 2013 .

[9]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[10]  Mustafa Bayram Gücen,et al.  Practical stability in terms of two measures for fractional order dynamic systems in Caputo's sense with initial time difference , 2014, J. Frankl. Inst..

[11]  Ivanka M. Stamova,et al.  Impulsive control on the asymptotic stability of the solutions of a Solow model with endogenous labor growth , 2012, J. Frankl. Inst..

[12]  Ivanka M. Stamova.  Impulsive control for stability of n-species Lotka-Volterra cooperation models with finite delays , 2010, Appl. Math. Lett..

[13]  Qingling Zhang,et al.  PRACTICAL STABILIZATION AND CONTROLLABILITY OF DESCRIPTOR SYSTEMS , 2005 .

[14]  Shangbo Zhou,et al.  Chaos control and synchronization in a fractional neuron network system , 2008 .

[15]  V. Lakshmikantham,et al.  Stability Analysis of Nonlinear Systems , 1988 .

[16]  Yong Zhou,et al.  On the concept and existence of solution for impulsive fractional differential equations , 2012 .

[17]  Ivanka M. Stamova.  Global stability of impulsive fractional differential equations , 2014, Appl. Math. Comput..

[18]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[19]  Fei Wang,et al.  Asymptotic stability of delayed fractional-order neural networks with impulsive effects , 2015, Neurocomputing.

[20]  JinRong Wang,et al.  On recent developments in the theory of boundary value problems for impulsive fractional differential equations , 2012, Comput. Math. Appl..

[21]  JinRong Wang,et al.  Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations , 2012, Journal of Optimization Theory and Applications.

[22]  Ivanka M. Stamova.  Mittag-Leffler stability of impulsive differential equations of fractional order , 2015 .

[23]  Xiaodi Li,et al.  Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Ivanka M. Stamova,et al.  Asymptotic stability of impulsive control neutral-type systems , 2014, Int. J. Control.

[25]  Michal Fečkan,et al.  Stability analysis of impulsive fractional-order systems by vector comparison principle , 2015 .

[26]  Liao Xiao-feng,et al.  Impulsive Control for Fractional-Order Chaotic Systems , 2008 .

[27]  Zhenhai Liu,et al.  Feedback control for fractional impulsive evolution systems , 2015, Appl. Math. Comput..

[28]  Liping Chen,et al.  Synchronization of a Class of Fractional-Order Chaotic Neural Networks , 2013, Entropy.

[29]  JinRong Wang,et al.  Approximate mild solutions of fractional stochastic evolution equations in Hilbert spaces , 2015, Appl. Math. Comput..

[30]  Bingo Wing-Kuen Ling,et al.  Nonconvex integer optimal robust impulsive control strategy for first-order piecewise finite precision nonlinear random early detection algorithm. , 2012, ISA transactions.

[31]  Eva Kaslik,et al.  Nonlinear dynamics and chaos in fractional-order neural networks , 2012, Neural Networks.

[32]  I. Stamova.  Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations , 2007 .

[33]  Aihua Hu,et al.  Exponential synchronization of fractional-order complex networks via pinning impulsive control , 2015 .

[34]  Song Zheng.  Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays. , 2015, ISA transactions.

[35]  G. Stamov,et al.  Almost Periodic Solutions of Impulsive Differential Equations , 2012 .

[36]  Ivanka M. Stamova,et al.  Second method of Lyapunov and almost periodic solutions for impulsive differential systems of fractional order , 2015 .

[37]  Katrin Rohlf,et al.  Impulsive control of a Lotka-Volterra system , 1998 .

[38]  Lee H. Keel,et al.  Optimal practical stabilization and controllability of systems with Markovian jumps , 2003 .

[39]  Qidi Wu,et al.  Impulsive control of a financial model , 2005 .