Passivity-based non-fragile control for Markovian jump delayed systems via stochastic sampling

ABSTRACT This paper studies the problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling. The Markovian jumping parameters, appearing in the connection weight matrices and in two additive time-varying delay components, are considered to be different. The controller is assumed to have either additive or multiplicative norm-bounded uncertainties. The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional. This functional fully utilises the sawtooth structure characteristics of the sampling input delay. By using the matrix decomposition method and some newly inequalities, sufficient conditions are obtained to guarantee that for all admissible uncertainties the system is robustly stochastically passive. Illustrative examples are provided to show the effectiveness of the results.

[1]  B. Francis,et al.  Input-output stability of sampled-data systems , 1991 .

[2]  Wu-Hua Chen,et al.  Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays , 2004, Syst. Control. Lett..

[3]  Qing Zhao,et al.  Norm invariant discretization for sampled-data fault detection , 2005, Autom..

[4]  Zidong Wang,et al.  State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays ☆ , 2008 .

[5]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[6]  Yonggang Chen,et al.  Improved Results on Passivity Analysis of Uncertain Neural Networks with Time-Varying Discrete and Distributed Delays , 2009, Neural Processing Letters.

[7]  Zhang Qing-ling,et al.  Stochastic stability of networked control systems with time-varying sampling periods , 2009 .

[8]  James Lam,et al.  New passivity criteria for neural networks with time-varying delay , 2009, Neural Networks.

[9]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[11]  P. Balasubramaniam,et al.  Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays ☆ , 2010 .

[12]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[14]  Huijun Gao,et al.  Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks With Defective Statistics of Modes Transitions , 2011, IEEE Transactions on Neural Networks.

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

[16]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[17]  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.

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

[19]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[20]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[21]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

[22]  Jinde Cao,et al.  Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms , 2013, Neural Processing Letters.

[23]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[24]  Jun Cheng,et al.  Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays , 2014, Appl. Math. Comput..

[25]  Shengyuan Xu,et al.  Relaxed passivity conditions for neural networks with time-varying delays , 2014, Neurocomputing.

[26]  Jun Cheng,et al.  H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays. , 2014, ISA transactions.

[27]  Frédéric Gouaisbaut,et al.  Complete Quadratic Lyapunov functionals using Bessel-Legendre inequality , 2014, 2014 European Control Conference (ECC).

[28]  R. Rakkiyappan,et al.  Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control , 2015, J. Frankl. Inst..

[29]  Shuping He,et al.  Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls , 2015, Neurocomputing.

[30]  Jinde Cao,et al.  Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach , 2015, Neural Networks.

[31]  Ju H. Park,et al.  Non-fragile Observer-Based $${\mathcal {H}}_{\infty }$$H∞ Control for Discrete-Time Systems Using Passivity Theory , 2015, Circuits Syst. Signal Process..

[32]  Guoliang Chen,et al.  Improved passivity analysis for neural networks with Markovian jumping parameters and interval time-varying delays , 2015, Neurocomputing.

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

[34]  Renquan Lu,et al.  Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling , 2015, Syst. Control. Lett..

[35]  Z. Yuping,et al.  State estimation of recurrent neural networks with two Markovian jumping parameters and mixed delays , 2015, 2015 34th Chinese Control Conference (CCC).

[36]  Shouming Zhong,et al.  State estimation for uncertain Markovian jump neural networks with mixed delays , 2016, Neurocomputing.

[37]  Shengyuan Xu,et al.  Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay , 2016 .

[38]  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..

[39]  Shouming Zhong,et al.  New passivity criteria for uncertain neural networks with time-varying delay , 2016, Neurocomputing.

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

[41]  Zheng-Guang Wu,et al.  Filtering for Discrete-Time Switched Fuzzy Systems With Quantization , 2017, IEEE Transactions on Fuzzy Systems.

[42]  Renquan Lu,et al.  Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Xinzhi Liu,et al.  Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. , 2017, ISA transactions.

[44]  Peng Shi,et al.  Reliable Control of Fuzzy Systems With Quantization and Switched Actuator Failures , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[45]  Peng Shi,et al.  Passivity-Based Asynchronous Control for Markov Jump Systems , 2017, IEEE Transactions on Automatic Control.

[46]  Peng Shi,et al.  Finite-Time Distributed State Estimation Over Sensor Networks With Round-Robin Protocol and Fading Channels , 2018, IEEE Transactions on Cybernetics.

[47]  Peng Shi,et al.  Robust Estimation for Neural Networks With Randomly Occurring Distributed Delays and Markovian Jump Coupling , 2018, IEEE Transactions on Neural Networks and Learning Systems.