Dissipativity Analysis for Neural Networks With Time-Varying Delays via a Delay-Product-Type Lyapunov Functional Approach

This article is concerned with the problem of dissipativity and stability analysis for a class of neural networks (NNs) with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional (LKF), including some delay-product-type terms, is proposed, in which the information on time-varying delay and system states is taken into full consideration. Second, by employing a generalized free-matrix-based inequality and its simplified version to estimate the derivative of the proposed LKF, some improved delay-dependent conditions are derived to ensure that the considered NNs are strictly (Q, S, R)-ɣ-dissipative. Furthermore, the obtained results are applied to passivity and stability analysis of delayed NNs. Finally, two numerical examples and a real-world problem in the quadruple tank process are carried out to illustrate the effectiveness of the proposed method.

[1]  Qing-Long Han,et al.  Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components , 2017, IEEE Transactions on Cybernetics.

[2]  Renquan Lu,et al.  Finite-Horizon $H_{\infty}$ State Estimation for Periodic Neural Networks Over Fading Channels , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Huaicheng Yan,et al.  Input–output finite-time mean square stabilization of nonlinear semi-Markovian jump systems , 2019, Automatica.

[4]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[5]  Qing-Long Han,et al.  Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Qing-Long Han,et al.  An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay , 2017, Autom..

[7]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[8]  Ju H. Park,et al.  Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties , 2012 .

[9]  F. M. Callier,et al.  Dissipative Systems Analysis and Control: Theory and Applications (2nd Edition)-[Book review; B. Brogliato, R. Lozano, B. Maschke] , 2007, IEEE Transactions on Automatic Control.

[10]  James Lam,et al.  α-Dissipativity analysis of singular time-delay systems , 2011, Autom..

[11]  K. Teo,et al.  Sampled-data-based dissipative control of T-S fuzzy systems , 2019, Applied Mathematical Modelling.

[12]  Jinde Cao,et al.  Exponential stability and extended dissipativity criteria for generalized neural networks with interval time-varying delay signals , 2017, J. Frankl. Inst..

[13]  Alexandre Seuret,et al.  Stability of Linear Systems With Time-Varying Delays Using Bessel–Legendre Inequalities , 2018, IEEE Transactions on Automatic Control.

[14]  Jianwei Xia,et al.  Further results on dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties , 2015 .

[15]  Gang Feng,et al.  Robust cooperative output regulation of multi-agent systems via adaptive event-triggered control , 2019, Autom..

[16]  Ju H. Park,et al.  Stability and dissipativity analysis of static neural networks with interval time-varying delay , 2015, J. Frankl. Inst..

[17]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[18]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[19]  Jun Wang,et al.  A Bi-Projection Neural Network for Solving Constrained Quadratic Optimization Problems , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Rathinasamy Sakthivel,et al.  Dissipative analysis for discrete-time systems via fault-tolerant control against actuator failures , 2016, Complex..

[21]  Fuwen Yang,et al.  Event-Triggered Asynchronous Guaranteed Cost Control for Markov Jump Discrete-Time Neural Networks With Distributed Delay and Channel Fading , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Hongyi Li,et al.  Event-Triggered Control for Multiagent Systems With Sensor Faults and Input Saturation , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[23]  Karl Henrik Johansson,et al.  The quadruple-tank process: a multivariable laboratory process with an adjustable zero , 2000, IEEE Trans. Control. Syst. Technol..

[24]  Derui Ding,et al.  An overview of recent developments in Lyapunov-Krasovskii functionals and stability criteria for recurrent neural networks with time-varying delays , 2018, Neurocomputing.

[25]  Min Wu,et al.  Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach , 2017, Appl. Math. Comput..

[26]  Raman Manivannan,et al.  Further improved results on stability and dissipativity analysis of static impulsive neural networks with interval time-varying delays , 2017, J. Frankl. Inst..

[27]  Yong He,et al.  Extended Dissipativity Analysis for Markovian Jump Neural Networks With Time-Varying Delay via Delay-Product-Type Functionals , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[28]  Zhigang Zeng,et al.  Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel–Legendre Inequalities , 2018, IEEE Transactions on Cybernetics.

[29]  Renquan Lu,et al.  Adaptive Neural Network Tracking Control for Robotic Manipulators With Dead Zone , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Ju H. Park,et al.  Stability Analysis of Neural Networks With Time-Varying Delay by Constructing Novel Lyapunov Functionals , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[32]  Min Wu,et al.  Dissipativity analysis of neural networks with time-varying delays , 2015, Neurocomputing.

[33]  Bin Yang,et al.  Further results on passivity analysis for uncertain neural networks with discrete and distributed delays , 2018, Inf. Sci..

[34]  Kok Lay Teo,et al.  New insights on stability of sampled-data systems with time-delay , 2020, Appl. Math. Comput..

[35]  Peng Shi,et al.  Dissipativity-Based Reliable Control for Fuzzy Markov Jump Systems With Actuator Faults , 2017, IEEE Transactions on Cybernetics.

[36]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[37]  Qing-Long Han,et al.  Passivity Analysis of Delayed Neural Networks Based on Lyapunov–Krasovskii Functionals With Delay-Dependent Matrices , 2020, IEEE Transactions on Cybernetics.

[38]  Zhen Wang,et al.  Further results on sampled-data synchronization control for chaotic neural networks with actuator saturation , 2019, Neurocomputing.

[39]  Yong He,et al.  Passivity analysis for neural networks with a time-varying delay , 2011, Neurocomputing.

[40]  Hong-Bing Zeng,et al.  A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems , 2019, Appl. Math. Comput..

[41]  Hong-Hai Lian,et al.  Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality , 2017 .

[42]  Rathinasamy Sakthivel,et al.  Dissipativity based repetitive control for switched stochastic dynamical systems , 2016, Appl. Math. Comput..

[43]  Fei Long,et al.  Dissipativity analysis for neural networks with two-delay components using an extended reciprocally convex matrix inequality , 2018, Inf. Sci..

[44]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[45]  Hamid Reza Karimi,et al.  New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[46]  Renquan Lu,et al.  Event-Triggered Consensus Control for Multi-Agent Systems Against False Data-Injection Attacks , 2019, IEEE Transactions on Cybernetics.

[47]  Xinge Liu,et al.  Dissipativity analysis for generalized neural networks with Markovian jump parameters and time-varying delay , 2017 .

[48]  James Lam,et al.  Stability and Dissipativity Analysis of Static Neural Networks With Time Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.