Fixed-time stability and stabilization of impulsive dynamical systems

Abstract This paper mainly tends to consider the fixed-time stability behavior for impulsive dynamical systems. An efficient theorem is established to construct an impulsive comparison system. By means of inequality analysis method, certain average impulsive interval and Lyapunov function, some sufficient conditions are given to ensure the fixed-time stability of impulsive dynamical systems. Moreover, as an important application, the fixed-time stabilization of a class of coupled impulsive neural networks is proposed. By designing a discontinuous control law, several new criteria are obtained to guarantee the fixed-time stabilization of the coupled impulsive neural networks. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.

[1]  Guanghui Wen,et al.  Distributed Robust Fixed-Time Consensus for Nonlinear and Disturbed Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  Jinde Cao,et al.  Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks , 2016, IEEE Transactions on Cybernetics.

[3]  Xinsong Yang,et al.  Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects , 2016, IEEE Transactions on Automatic Control.

[4]  Michael Z. Q. Chen,et al.  On finite-time stability for nonlinear impulsive switched systems , 2013 .

[5]  Piyapong Niamsup,et al.  Finite-time stability of singular nonlinear switched time-delay systems: A singular value decomposition approach , 2017, J. Frankl. Inst..

[6]  Yang Liu,et al.  Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems. , 2015, ISA transactions.

[7]  Remco I. Leine,et al.  Global uniform symptotic attractive stability of the non-autonomous bouncing ball system , 2012 .

[8]  Francesco Amato,et al.  Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems , 2013, Autom..

[9]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[10]  Guang-Ren Duan,et al.  Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity , 2017, J. Frankl. Inst..

[11]  Yijing Wang,et al.  Finite-time stabilization of switched nonlinear systems with partial unstable modes , 2016, Appl. Math. Comput..

[12]  Zhengrong Xiang,et al.  Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form , 2017, J. Frankl. Inst..

[13]  Jinde Cao,et al.  Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks , 2016, Neural Networks.

[14]  Guopei Chen,et al.  Finite time stability of a class of hybrid dynamical systems , 2012 .

[15]  Hamid Reza Karimi,et al.  Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays , 2014, Circuits Syst. Signal Process..

[16]  Sergey G. Nersesov,et al.  Finite-time coordination in multiagent systems using sliding mode control approach , 2013, ACC.

[17]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

[18]  Tingwen Huang,et al.  Second-Order Continuous-Time Algorithms for Economic Power Dispatch in Smart Grids , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[19]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[20]  Donal O'Regan,et al.  Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays , 2015 .

[21]  Tingwen Huang,et al.  Passivity and Output Synchronization of Complex Dynamical Networks With Fixed and Adaptive Coupling Strength , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Ting Li,et al.  A new approach to fast global finite-time stabilization of high-order nonlinear system , 2017, Autom..

[23]  Andrey Polyakov,et al.  Finite-time and fixed-time stabilization: Implicit Lyapunov function approach , 2015, Autom..

[24]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[25]  Jinde Cao,et al.  Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control , 2017, Neural Networks.

[26]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Tianping Chen,et al.  A note on finite-time and fixed-time stability , 2015, Neural Networks.

[28]  W. Haddad,et al.  Finite-time stabilization of nonlinear impulsive dynamical systems☆ , 2008 .

[29]  James Lam,et al.  Fixed-Time Synchronization of Complex Networks With Impulsive Effects via Nonchattering Control , 2017, IEEE Transactions on Automatic Control.

[30]  Xiaoyu Hu,et al.  Fast Fixed-Time Nonsingular Terminal Sliding Mode Control and Its Application to Chaos Suppression in Power System , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  Tianping Chen,et al.  Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control , 2018, IEEE Transactions on Cybernetics.

[33]  Tingwen Huang,et al.  Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks , 2017, Neural Networks.

[34]  Wassim M. Haddad,et al.  Finite-time stabilization of nonlinear impulsive dynamical systems , 2007, 2007 European Control Conference (ECC).

[35]  Guangdeng Zong,et al.  Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems , 2014, CCC 2014.

[36]  A. Kartsatos.  Advanced Ordinary Differential Equations , 1980 .

[37]  Garrett M. Clayton,et al.  Finite-time tracking using sliding mode control , 2012, J. Frankl. Inst..

[38]  Z. Zuo,et al.  Non-singular fixed-time terminal sliding mode control of non-linear systems , 2015 .

[39]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..