A new fixed-time stability theorem and its application to the synchronization control of memristive neural networks

Abstract In this paper, we propose a new fixed-time stability theorem. Numerical simulations show that our upper bound estimate for the settling time is much smaller than those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, we investigate the fixed-time synchronization of memristive neural networks (MNNs) by adopting a delay-dependent feedback controller. Numerical simulations are provided to demonstrate the correctness of our theoretical results and the superiority of the new fixed-time stability theorem.

[1]  Xiaofan Li,et al.  Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays , 2017, Neurocomputing.

[2]  Shouming Zhong,et al.  Novel master-slave synchronization criteria of chaotic Lur'e systems with time delays using sampled-data control , 2017, J. Frankl. Inst..

[3]  Lihong Huang,et al.  Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[4]  V. Haimo.  Finite time controllers , 1986 .

[5]  Chuandong Li,et al.  Fixed-time stability and stabilization of impulsive dynamical systems , 2017, J. Frankl. Inst..

[6]  Haijun Jiang,et al.  Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design , 2018, J. Frankl. Inst..

[7]  Zhigang Zeng,et al.  Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations , 2017, Neural Networks.

[8]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[9]  Xin-Ping Guan,et al.  Finite/Fixed-Time Stabilization for Nonlinear Interconnected Systems With Dead-Zone Input , 2017, IEEE Transactions on Automatic Control.

[10]  Jun Wang,et al.  Global Exponential Synchronization of Multiple Memristive Neural Networks With Time Delay via Nonlinear Coupling , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Jinde Cao,et al.  Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions , 2017, Neural Networks.

[12]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[13]  Michael I. Friswell,et al.  Fixed-Time Attitude Control for Rigid Spacecraft With Actuator Saturation and Faults , 2016, IEEE Transactions on Control Systems Technology.

[14]  Fuad E. Alsaadi,et al.  Fixed-Time Synchronization of Coupled Discontinuous Neural Networks with Nonidentical Perturbations , 2017, Neural Processing Letters.

[15]  Jinde Cao,et al.  An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications , 2017, IEEE Transactions on Automatic Control.

[16]  Xiaofan Li,et al.  Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays , 2018, International Journal of Adaptive Control and Signal Processing.

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

[18]  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.

[19]  Wassim M. Haddad,et al.  Finite-Time Stabilization of Nonlinear Dynamical Systems via Control Vector Lyapunov Functions , 2007, 2007 American Control Conference.

[20]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[21]  Peng Shi,et al.  Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems , 2016, IEEE Transactions on Cybernetics.

[22]  Shouming Zhong,et al.  Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays , 2017, Appl. Math. Comput..

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

[24]  Daniel W. C. Ho,et al.  Finite/Fixed-Time Pinning Synchronization of Complex Networks With Stochastic Disturbances , 2019, IEEE Transactions on Cybernetics.

[25]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[26]  Shouming Zhong,et al.  Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays , 2017, Neurocomputing.

[27]  Pavel Shcherbakov,et al.  Nonlinear fixed-time control protocol for uniform allocation of agents on a segment , 2013 .

[28]  Hongmin Li,et al.  Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Nonsmooth Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

[29]  Haipeng Peng,et al.  Adaptive Lag Synchronization of Memristive Neural Networks With Mixed Delays , 2018, IEEE Access.

[30]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

[31]  Guang-Hong Yang,et al.  New Results on Output Feedback $H_{\infty} $ Control for Linear Discrete-Time Systems , 2014, IEEE Transactions on Automatic Control.

[32]  Xiaoming Han,et al.  Adaptive exponential synchronization of memristive neural networks with mixed time-varying delays , 2016, Neurocomputing.

[33]  Chuan Chen,et al.  Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay , 2017, Neural Networks.

[34]  Yuhua Xu,et al.  A class of fast fixed-time synchronization control for the delayed neural network , 2018, J. Frankl. Inst..

[35]  Xiaofan Li,et al.  Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control , 2017, Neural Networks.

[36]  Chuandong Li,et al.  Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control , 2019, IEEE Transactions on Cybernetics.

[37]  Lihong Huang,et al.  New conditions on synchronization of memristor-based neural networks via differential inclusions , 2016, Neurocomputing.

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

[39]  Chuandong Li,et al.  Fixed-time stabilization of impulsive Cohen-Grossberg BAM neural networks , 2018, Neural Networks.

[40]  Xiaofan Li,et al.  Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions , 2018, Neurocomputing.

[41]  L. Chua.  Memristor-The missing circuit element , 1971 .

[42]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[43]  Shouming Zhong,et al.  New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems , 2018, Nonlinear Analysis: Hybrid Systems.

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

[45]  Ju H. Park,et al.  Fuzzy Resilient Energy-to-Peak Filtering for Continuous-Time Nonlinear Systems , 2017, IEEE Transactions on Fuzzy Systems.

[46]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[47]  Chuan Chen,et al.  Adaptive synchronization of memristor-based BAM neural networks with mixed delays , 2018, Appl. Math. Comput..

[48]  Chuan Chen,et al.  Finite-time synchronization of memristor-based neural networks with mixed delays , 2017, Neurocomputing.

[49]  Xinzhi Liu,et al.  A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems , 2017, Fuzzy Sets Syst..

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

[51]  Lixiang Li,et al.  Fixed-time synchronization of inertial memristor-based neural networks with discrete delay , 2019, Neural Networks.

[52]  Xiao-Heng Chang,et al.  Peak-to-Peak Filtering for Networked Nonlinear DC Motor Systems With Quantization , 2018, IEEE Transactions on Industrial Informatics.

[53]  Wilfrid Perruquetti,et al.  Finite time stability conditions for non-autonomous continuous systems , 2008, Int. J. Control.

[54]  Sanjay P. Bhat,et al.  Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria , 2009, IEEE Transactions on Automatic Control.

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

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