Reachable set estimation for Markovian jump neural networks with time-varying delay

This paper is concerned with the reachable set estimation for Markovian jump neural networks with time-varying delay and bounded peak inputs. The objective is to find a description of a reachable set that is containing all reachable states starting from the origin. In the framework of Lyapunov-Krasovskii functional method, an appropriate Lyapunov-Krasovskii functional is constructed firstly. Then by using the Wirtinger-based integral inequality and the extended reciprocally convex matrix inequality, an ellipsoidal description of the reachable set for the considered neural networks is derived. Finally, a numerical example with simulation results is provided to verify the effectiveness of our results.

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

[2]  James Lam,et al.  An improved result on reachable set estimation and synthesis of time-delay systems , 2014, Appl. Math. Comput..

[3]  Qing-Long Han,et al.  Global Asymptotic Stability for Delayed Neural Networks Using an Integral Inequality Based on Nonorthogonal Polynomials , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[5]  Qing-Guo Wang,et al.  Stability Analysis of Discrete-Time Neural Networks With Time-Varying Delay via an Extended Reciprocally Convex Matrix Inequality , 2017, IEEE Transactions on Cybernetics.

[6]  Jinde Cao,et al.  Stability of Markovian jump neural networks with impulse control and time varying delays , 2012 .

[7]  Emilia Fridman,et al.  On reachable sets for linear systems with delay and bounded peak inputs , 2003, Autom..

[8]  Zheng-Guang Wu,et al.  Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays , 2017, IEEE Transactions on Cybernetics.

[9]  M. Syed Ali,et al.  Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays , 2015, Neurocomputing.

[10]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[11]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Min Wu,et al.  An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay , 2017, Autom..

[13]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

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

[15]  Shengyuan Xu,et al.  Reachable set estimation for discrete‐time linear systems with time delays , 2015 .

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

[17]  Guoliang Chen,et al.  Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components , 2016, J. Frankl. Inst..

[18]  Changchun Hua,et al.  Adaptive Fuzzy Prescribed Performance Control for Nonlinear Switched Time-Delay Systems With Unmodeled Dynamics , 2018, IEEE Transactions on Fuzzy Systems.

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

[20]  Daniel W. C. Ho,et al.  Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach , 2010, Autom..

[21]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Yijing Wang,et al.  A non-ellipsoidal reachable set estimation for uncertain neural networks with time-varying delay , 2014, Commun. Nonlinear Sci. Numer. Simul..

[23]  Wei Xing Zheng,et al.  On reachable set estimation of delay Markovian jump systems with partially known transition probabilities , 2016, J. Frankl. Inst..

[24]  Jin-Hoon Kim,et al.  Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances , 2008, Autom..

[25]  Guoliang Chen,et al.  Extended dissipative analysis of generalized Markovian switching neural networks with two delay components , 2017, Neurocomputing.

[26]  Min Wu,et al.  Stability analysis of recurrent neural networks with interval time-varying delay via free-matrix-based integral inequality , 2016, Neurocomputing.

[27]  Frédéric Gouaisbaut,et al.  Hierarchy of LMI conditions for the stability analysis of time-delay systems , 2015, Syst. Control. Lett..

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

[29]  Xin-Ping Guan,et al.  On Exploring the Domain of Attraction for Bilateral Teleoperator Subject to Interval Delay and Saturated P + d Control Scheme , 2017, IEEE Transactions on Automatic Control.

[30]  Muthukumar Palanisamy,et al.  Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination , 2016, Neurocomputing.

[31]  Shengyuan Xu,et al.  Relaxed results on reachable set estimation of time‐delay systems with bounded peak inputs , 2016 .

[32]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[33]  Quanxin Zhu,et al.  An Improved Result on Dissipativity and Passivity Analysis of Markovian Jump Stochastic Neural Networks With Two Delay Components , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Hieu Minh Trinh,et al.  Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances , 2018, Neural Computing and Applications.