Extended dissipative asynchronous filtering for T–S fuzzy switched systems with partial transition descriptions and incomplete measurements

Abstract This paper analyzes the problem of extended dissipative asynchronous filtering for Markov jump T–S fuzzy systems (MJTSFSs) with sensor failures and incomplete measurements. The highlight of this work lies in the fact that we introduce an asynchronous filter (AF) in which mode transition probability matrix (TPM) is non-homogeneous. “Asynchronous” means that the switching of the filters to be designed may be different from that of the systems. Thanks to this AF, partial information of system modes can be fully utilized to achieve the improved and extended dissipative performance including the dissipativity, passivity, H ∞ performance and l 2 − l ∞ performance. Specifically, we first attempt to show that the transition probability information (TPI) of the two different Markov chains is not fully known, which can be regarded as an extension of existing work. In the meantime, this is also an arduous problem to be solved in this article. Additionally, with respect to the asynchronous filtering of MJTSFSs, we not only consider that sensor failures occur randomly in the filter systems, but also that research that the measured output is assumed to be quantized by the logarithmic quantizer. Then, an AF is designed for MJTSFSs with sensor failures and incomplete transition probability (ITP) for the first time. Finally, through three examples, the effects of sensor failures, quantizers, and degrees of asynchronism on system performance are examined.

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

[2]  Lei Zou,et al.  Ultimate Boundedness Control for Networked Systems With Try-Once-Discard Protocol and Uniform Quantization Effects , 2017, IEEE Transactions on Automatic Control.

[3]  Xin Wang,et al.  Delay-Dependent Fuzzy Sampled-Data Synchronization of T–S Fuzzy Complex Networks With Multiple Couplings , 2020, IEEE Transactions on Fuzzy Systems.

[4]  Peng Shi,et al.  Asynchronous Filtering for Markov Jump Neural Networks With Quantized Outputs , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[6]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Peng Shi,et al.  Asynchronous Filtering of Nonlinear Markov Jump Systems With Randomly Occurred Quantization via T–S Fuzzy Models , 2018, IEEE Transactions on Fuzzy Systems.

[8]  Jingli Ren,et al.  A repeated yielding model under periodic perturbation , 2018, Nonlinear Dynamics.

[9]  Jun Wang,et al.  Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies , 2020, Fuzzy Sets Syst..

[10]  Kun She,et al.  Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays , 2018, Appl. Math. Comput..

[11]  Hong Cheng,et al.  Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays , 2019, Appl. Math. Comput..

[12]  Shouming Zhong,et al.  Extended dissipative conditions for memristive neural networks with multiple time delays , 2018, Appl. Math. Comput..

[13]  Wenyong Wang,et al.  Event-triggered passive control for Markovian jump discrete-time systems with incomplete transition probability and unreliable channels , 2019, J. Frankl. Inst..

[14]  Fuad E. Alsaadi,et al.  Output-Feedback Control for Nonlinear Stochastic Systems With Successive Packet Dropouts and Uniform Quantization Effects , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[15]  R. Evans,et al.  Stabilization with data-rate-limited feedback: tightest attainable bounds , 2000 .

[16]  Yugang Niu,et al.  Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities , 2018, Autom..

[17]  Hamid Reza Karimi,et al.  Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition , 2019, International Journal of Robust and Nonlinear Control.

[18]  Bruce A. Francis,et al.  Limited Data Rate in Control Systems with Networks , 2002 .

[19]  Jian-Ning Li,et al.  Finite-time non-fragile state estimation for discrete neural networks with sensor failures, time-varying delays and randomly occurring sensor nonlinearity , 2019, J. Frankl. Inst..

[20]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[21]  Xinzhi Liu,et al.  A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems , 2017, Fuzzy Sets Syst..

[22]  Jie Lian,et al.  T–S Fuzzy Control of Positive Markov Jump Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

[23]  Dan Ye,et al.  Finite frequency fault detection for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures , 2019, Nonlinear Dynamics.

[24]  Shengyuan Xu,et al.  Observer-based mixed passive and H∞ control for uncertain Markovian jump systems with time delays using quantized measurements , 2019, Nonlinear Analysis: Hybrid Systems.

[25]  Yajuan Liu,et al.  Asynchronous output feedback dissipative control of Markovian jump systems with input time delay and quantized measurements , 2019, Nonlinear Analysis: Hybrid Systems.

[26]  Dan Zhang,et al.  Asynchronous and Resilient Filtering for Markovian Jump Neural Networks Subject to Extended Dissipativity , 2019, IEEE Transactions on Cybernetics.

[27]  Kun She,et al.  Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays , 2018, Appl. Math. Comput..

[28]  Nam Kyu Kwon,et al.  H∞ control for Markovian jump fuzzy systems with partly unknown transition rates and input saturation , 2018, J. Frankl. Inst..

[29]  Shouming Zhong,et al.  Novel results on dissipativity analysis for generalized delayed neural networks , 2019, Neurocomputing.

[30]  James Lam,et al.  H∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach , 2007, Fuzzy Sets Syst..

[31]  Zhen Wang,et al.  Quantized asynchronous dissipative state estimation of jumping neural networks subject to occurring randomly sensor saturations , 2018, Neurocomputing.

[32]  S. Nguang,et al.  H/sub /spl infin// filtering for fuzzy dynamical systems with D stability constraints , 2003 .

[33]  Yindong Ji,et al.  Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements , 2016 .

[34]  Wei Xing Zheng,et al.  On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Shouming Zhong,et al.  Extended dissipative state estimation for memristive neural networks with time-varying delay. , 2016, ISA transactions.

[36]  Peng Shi,et al.  Quantized Control of Markov Jump Nonlinear Systems Based on Fuzzy Hidden Markov Model , 2019, IEEE Transactions on Cybernetics.

[37]  Hamid Reza Karimi,et al.  Universal adaptive control for uncertain nonlinear systems via output feedback , 2019, Inf. Sci..

[38]  Tieshan Li,et al.  Fuzzy-approximation adaptive fault-tolerant control for nonlinear pure-feedback systems with unknown control directions and sensor failures , 2019, Fuzzy Sets Syst..

[39]  Jinde Cao,et al.  An Event-Based Asynchronous Approach to Markov Jump Systems With Hidden Mode Detections and Missing Measurements , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[40]  Shengyuan Xu,et al.  Reliable exponential H∞ filtering for singular Markovian jump systems with time‐varying delays and sensor failures , 2018, International Journal of Robust and Nonlinear Control.

[41]  Yuxin Zhao,et al.  Resilient Asynchronous $H_{\infty }$ Filtering for Markov Jump Neural Networks With Unideal Measurements and Multiplicative Noises , 2015, IEEE Transactions on Cybernetics.

[42]  Donghua Zhou,et al.  Event-triggered resilient filtering with measurement quantization and random sensor failures: Monotonicity and convergence , 2018, Autom..