Reachable set estimation for inertial Markov jump BAM neural network with partially unknown transition rates and bounded disturbances

Abstract This paper mainly focuses on the reachable set estimation problem of a time-varying delayed inertial Markov jump bidirectional associative memory (BAM) neural network with bounded disturbance inputs. The disturbances are assumed to be either unit-energy bounded or unit-peak bounded. Different from systems of the past studies, this paper is for inertial Markov jump BAM neural network with both time-varying delay and time-varying transition rates. The time-varying character of the considered transition rates is assumed to be piecewise-constant. In order to reduce the conservatism, the delay-partitioning technique is utilized to solve this reachable set estimation problem. As a result, it is obtained that the ellipsoid defined in this paper contains the reachable set R u p , which indicates the reachable set R u e is included. Further, we extend the results to the uncertain Markov jump BAM neutral network with partially unknown transition probabilities. Numerical examples are proposed to show the effectiveness of the given results.

[1]  Daniel W. C. Ho,et al.  A note on reachable set bounding for delayed systems with polytopic uncertainties , 2013, J. Frankl. Inst..

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

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

[4]  Magdi S. Mahmoud,et al.  $H_\infty$ and robust control of interconnected systems with Markovian jump parameters , 2005 .

[5]  Shengyuan Xu,et al.  Reachable set estimation and controller design for distributed delay systems with bounded disturbances , 2014, J. Frankl. Inst..

[6]  Hongsheng Xi,et al.  On exponential stability of neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates , 2014 .

[7]  H. Karimi,et al.  Quantized ℋ∞ Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information , 2015 .

[8]  R. Rakkiyappan,et al.  Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control , 2014, Neurocomputing.

[9]  James Lam,et al.  Stability and Stabilization for Markovian Jump Time-Delay Systems With Partially Unknown Transition Rates , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Pubudu N. Pathirana,et al.  Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays , 2011, Autom..

[11]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[12]  Hamid Reza Karimi,et al.  model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information , 2014, Int. J. Syst. Sci..

[13]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .

[14]  Youhua Fu,et al.  A new method of reachable set estimation for time delay systems with polytopic uncertainties , 2013, Appl. Math. Comput..

[15]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[16]  Xiaodi Li,et al.  Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays , 2011, Appl. Math. Comput..

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

[18]  Fei Liu,et al.  Finite-time filtering for non-linear stochastic systems with partially known transition jump rates , 2010 .

[19]  Quanxin Zhu,et al.  Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching , 2017, Int. J. Control.

[20]  Jinde Cao,et al.  Stability Analysis of Markovian Jump Stochastic BAM Neural Networks With Impulse Control and Mixed Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Sanjay Lall,et al.  Polynomial Level-Set Method for Polynomial System Reachable Set Estimation , 2013, IEEE Transactions on Automatic Control.

[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]  Caixia Liu,et al.  Robust finite-time stabilization of uncertain singular Markovian jump systems , 2012 .

[24]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[25]  Jianbin Qiu,et al.  A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[27]  Xinzhi Liu,et al.  Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities , 2012, J. Frankl. Inst..

[28]  Zhiguang Feng,et al.  Integral partitioning approach to robust stabilization for uncertain distributed time‐delay systems , 2012 .

[29]  Yijing Wang,et al.  New Criteria of Reachable Set Estimation for Time Delay Systems Subject to Polytopic Uncertainties , 2012, ROCOND.

[30]  Shouming Zhong,et al.  The ellipsoidal bound of reachable sets for linear neutral systems with disturbances , 2011, J. Frankl. Inst..

[31]  Xin Wang,et al.  Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control , 2015 .

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

[33]  Shouming Zhong,et al.  Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates , 2012, Appl. Math. Comput..

[34]  James Lam,et al.  On reachable set estimation of singular systems , 2015, Autom..

[35]  Qing-Long Han.  A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays , 2004, Autom..

[36]  Z. Zuo,et al.  Results on reachable set estimation for linear systems with both discrete and distributed delays , 2012 .

[37]  Yulong Xu,et al.  Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates , 2014, J. Frankl. Inst..

[38]  J.C. Geromel,et al.  ${\cal H}_{\infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities , 2009, IEEE Transactions on Automatic Control.