New criteria on periodicity and stabilization of discontinuous uncertain inertial Cohen-Grossberg neural networks with proportional delays

Abstract This paper is concerned with the periodicity and stabilization of a class of discontinuous uncertain inertial Cohen-Grossberg neural networks with proportional delays. First of all, based on the differential inclusions and coincidence theorem, some new proportional delay-dependent criteria are obtained for ensuring the existence of periodic solutions. It is the first result on the proportional delay-dependent criteria of delayed inertial neural networks (INNs). Secondly, in light of the definition of fixed-time (FXT) stable, the zero solution of the considered inertial neural model can achieve the FXT stabilization with the help of the designed discontinuous control laws. Finally, for the purpose of examining the correctness of the established results, one numerical example and illustrative simulations are provided.

[1]  Adel M. Alimi,et al.  Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication , 2019, Neurocomputing.

[2]  C. Budd,et al.  Review of ”Piecewise-Smooth Dynamical Systems: Theory and Applications by M. di Bernardo, C. Budd, A. Champneys and P. 2008” , 2020 .

[3]  Parameswaran Ramanathan,et al.  Proportional differentiated services: delay differentiation and packet scheduling , 2002, TNET.

[4]  Quanxin Zhu,et al.  Fixed-time synchronization analysis for discontinuous fuzzy inertial neural networks with parameter uncertainties , 2021, Neurocomputing.

[5]  Meng Zhang,et al.  Input-to-state stability for hybrid delayed systems with admissible edge-dependent switching signals , 2020, J. Frankl. Inst..

[6]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Tingwen Huang,et al.  Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control , 2018, Neurocomputing.

[8]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[9]  Zhidong Teng,et al.  Finite-time synchronization for fuzzy cellular neural networks with time-varying delays , 2016, Fuzzy Sets Syst..

[10]  Jingfeng Wang,et al.  Global Lagrange stability for inertial neural networks with mixed time-varying delays , 2017, Neurocomputing.

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

[12]  Yanbo Gao,et al.  Exponential stability in Lagrange sense for inertial neural networks with time-varying delays , 2019, Neurocomputing.

[13]  Fuad E. Alsaadi,et al.  Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties , 2021, Neurocomputing.

[14]  Fanchao Kong,et al.  Delay-dependent criteria for periodicity and exponential stability of inertial neural networks with time-varying delays , 2021, Neurocomputing.

[15]  Zhigang Zeng,et al.  Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays , 2020, Neural Networks.

[16]  Jinde Cao,et al.  Novel Finite-Time Synchronization Criteria for Inertial Neural Networks With Time Delays via Integral Inequality Method , 2019, IEEE Transactions on Neural Networks and Learning Systems.

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

[18]  Mo Chen,et al.  Further study on finite-time synchronization for delayed inertial neural networks via inequality skills , 2020, Neurocomputing.

[19]  Zhengqiu Zhang,et al.  New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays , 2015, Neurocomputing.

[20]  Wanli Li,et al.  Exponential synchronization in inertial Cohen-Grossberg neural networks with time delays , 2019, J. Frankl. Inst..

[21]  Quanxin Zhu,et al.  New Fixed-Time Stability Lemmas and Applications to the Discontinuous Fuzzy Inertial Neural Networks , 2021, IEEE Transactions on Fuzzy Systems.

[22]  Tingwen Huang,et al.  Lagrange stability of delayed switched inertial neural networks , 2020, Neurocomputing.

[23]  Robert M. Westervelt,et al.  Stability and dynamics of simple electronic neural networks with added inertia , 1986 .

[24]  Zhigang Zeng,et al.  Passivity and Passification of Fuzzy Memristive Inertial Neural Networks on Time Scales , 2018, IEEE Transactions on Fuzzy Systems.

[25]  Kaibo Shi,et al.  Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method , 2020, Neural Networks.

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

[27]  R. Sriraman,et al.  Robust Passivity and Stability Analysis of Uncertain Complex-Valued Impulsive Neural Networks with Time-Varying Delays , 2021, Neural Processing Letters.

[28]  Jian Xu,et al.  Hopf bifurcation and chaos in an inertial neuron system with coupled delay , 2013 .

[29]  Zhigang Zeng,et al.  On Exponential Stability of Delayed Discrete-Time Complex-Valued Inertial Neural Networks. , 2020, IEEE transactions on cybernetics.

[30]  Chaouki Aouiti,et al.  Finite-Time and Fixed-Time Synchronization of Inertial Cohen–Grossberg-Type Neural Networks with Time Varying Delays , 2019, Neural Processing Letters.

[31]  Li Yong,et al.  Periodic solutions of differential inclusions , 1995 .

[32]  Chaouki Aouiti,et al.  Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations , 2019, Neurocomputing.

[33]  Jinde Cao,et al.  Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays , 2016, Neurocomputing.

[34]  Aouiti Chaouki,et al.  Finite-Time and Fixed-Time Synchronization of Inertial Neural Networks with Mixed Delays , 2020 .

[35]  Fuad E. Alsaadi,et al.  Passive filter design for fractional-order quaternion-valued neural networks with neutral delays and external disturbance , 2021, Neural Networks.

[36]  Fanchao Kong,et al.  New fixed‐time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov‐Krasovskii functional method , 2020, International Journal of Robust and Nonlinear Control.

[37]  Zhigang Zeng,et al.  Finite-time stabilization of memristor-based inertial neural networks with discontinuous activations and distributed delays , 2019, J. Frankl. Inst..