HMM‐based filtering for slow‐sampling singularly perturbed jumping systems

This study concentrates on the filtering for the slow-sampling jumping singularly perturbed systems, in which the situation that the filter mode is inconsistent with the system mode is taken into consideration. Based on the hidden-Markov model (HMM), such an asynchronous phenomenon between the system mode and the filter mode is depicted. Additionally, the unreliable communication channel resulting in packet loss is described through the assistance of a random variable. The authors' purpose is to design a filter that ensures the error system is extended stochastically dissipative. Moreover, with the aid of the Lyapunov stability theory and linear matrix inequality approach, a set of ϵ -independent conditions are derived to obtain the filter gains. Eventually, the effectiveness of the proposed method is demonstrated by a numerical example and a modified tunnel diode circuit model.

[1]  Wei Liu,et al.  Dynamic output feedback control for fast sampling discrete-time singularly perturbed systems , 2016 .

[2]  Fuchun Sun,et al.  Hinfinity control for fuzzy singularly perturbed systems , 2005, Fuzzy Sets Syst..

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

[4]  Jing Wang,et al.  Asynchronous dissipative filtering for nonlinear jumping systems subject to fading channels , 2020, J. Frankl. Inst..

[5]  Gang Feng,et al.  A New Switched System Approach to Leader–Follower Consensus of Heterogeneous Linear Multiagent Systems With DoS Attack , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[6]  Peng Shi,et al.  Robust Hinfinity fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: An LMI approach , 2007, Inf. Sci..

[7]  Wei Xing Zheng,et al.  HMM-Based $\mathcal{H}_{\infty}$ Filtering for Discrete-Time Markov Jump LPV Systems Over Unreliable Communication Channels , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Bugong Xu,et al.  Filter designing with finite packet losses and its application for stochastic systems , 2011 .

[9]  Christian Laugier,et al.  Incremental Learning of Statistical Motion Patterns With Growing Hidden Markov Models , 2007, IEEE Transactions on Intelligent Transportation Systems.

[10]  Yixin Yin,et al.  State feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems with parameter uncertainty , 2011 .

[11]  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.

[12]  Hao Shen,et al.  Non-fragile extended dissipativity-based state feedback control for 2-D Markov jump delayed systems , 2019, Appl. Math. Comput..

[13]  Jinde Cao,et al.  Network-Based Quantized Control for Fuzzy Singularly Perturbed Semi-Markov Jump Systems and its Application , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Erfu Yang,et al.  State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle , 2018, IET Control Theory & Applications.

[15]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[16]  James Lam,et al.  H∞ and H2 filtering for linear systems with uncertain Markov transitions , 2016, Autom..

[17]  Ligang Wu,et al.  Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[18]  Shengyuan Xu,et al.  Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations , 2018, IEEE Transactions on Automatic Control.

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

[20]  Fuad E. Alsaadi,et al.  Dynamic Event-Triggered State Estimation for Discrete-Time Singularly Perturbed Systems With Distributed Time-Delays , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[21]  Guanghong Yang,et al.  Robust H/sub /spl infin//1 control for standard discrete-time singularly perturbed systems , 2007 .

[22]  Chunyu Yang,et al.  Sampled-data H∞ filtering for Markovian jump singularly perturbed systems with time-varying delay and missing measurements , 2018, Int. J. Syst. Sci..

[23]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Discrete-Time Nonlinear Singularly Perturbed Complex Networks Under the Round-Robin Protocol , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Yugang Niu,et al.  Dynamic Event-Triggered Sliding Mode Control: Dealing With Slow Sampling Singularly Perturbed Systems , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[25]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

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

[27]  Hieu Minh Trinh,et al.  Robust stability of singularly perturbed discrete-delay systems , 1995, IEEE Trans. Autom. Control..

[28]  Guoliang Wang,et al.  Stabilisation bound of stochastic singularly perturbed systems with markovian switching by noise control , 2014 .

[29]  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.

[30]  P. Shi,et al.  Robust H1 control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach , 2007 .

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

[32]  Romain Postoyan,et al.  Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics , 2014, Autom..

[33]  Emilia Fridman Robust sampled-data H/sub /spl infin// control of linear singularly perturbed systems , 2006, IEEE Transactions on Automatic Control.

[34]  Shengyuan Xu,et al.  Resilient Asynchronous $H_{\infty}$ Control for Discrete-Time Markov Jump Singularly Perturbed Systems Based on Hidden Markov Model , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[35]  Ligang Wu,et al.  Filter design for discrete-time singularly perturbed T-S fuzzy systems , 2013, J. Frankl. Inst..

[36]  Jianwei Xia,et al.  Asynchronous H∞ filtering for nonlinear persistent dwell-time switched singular systems with measurement quantization , 2019, Appl. Math. Comput..

[37]  Guang-Hong Yang,et al.  H∞ control design for fuzzy discrete-time singularly perturbed systems via slow state variables feedback: An LMI-based approach , 2009, Inf. Sci..

[38]  Qingsong Liu,et al.  Stabilization of linear systems with both input and state delays by observer-predictors , 2017, Autom..

[39]  Emilia Fridman,et al.  A Novel Approach to Exact Slow-Fast Decomposition of Linear Singularly Perturbed Systems with Small Delays , 2017, SIAM J. Control. Optim..

[40]  Leszek Rutkowski,et al.  Sliding-Mode Control for Slow-Sampling Singularly Perturbed Systems Subject to Markov Jump Parameters , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[41]  Yueying Wang,et al.  A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems , 2018, Autom..

[42]  Biing-Hwang Juang,et al.  Maximum likelihood estimation for multivariate mixture observations of markov chains , 1986, IEEE Trans. Inf. Theory.