This paper investigates the problem of robust finite time extended passive reliable filtering for Takagi–Sugeno (T–S) fuzzy systems with randomly occurring uncertainties, missing measurements, and time-varying delays. Moreover, two stochastic variables satisfying the Bernoulli random distribution are introduced to characterize the phenomenon of the randomly occurring uncertainties and missing measurements. By skillfully choosing a proper Lyapunov–Krasovskii functional (LKF), a new set of sufficient conditions in terms of linear matrix inequalities (LMI) is derived to ensure that the filtering error system is robustly stochastically finite time bounded (SFTB) with a desired extended passive performance index. Based on the obtained sufficient conditions, an explicit expression for the desired filter can be computed. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design technique.
Issue Section:
Research Papers
Topics:
Errors,
Filters,
Filtration,
Fuzzy logic,
Theorems (Mathematics),
Delays,
Uncertainty,
Design
References
1.
Cheng
, J.
, Park
, J. H.
, Liu
, Y.
, Liu
, Z.
, and Tang
, L.
, 2017
, “Finite-Time Fuzzy Control of Nonlinear Markovian Jump Delayed Systems With Partly Uncertain Transition Descriptions
,” Fuzzy Sets Syst.
, 314
, pp. 99
–115
.2.
Ge
, X.
, Han
, Q.
, and Jiang
, X.
, 2014
, “Sampled-Data Filtering of Takagi-Sugeno Fuzzy Systems With Interval Time-Varying Delays
,” J. Franklin Inst.
, 351
(5
), pp. 2515
–2542
.3.
Wang
, H.
, Shi
, P.
, and Zhang
, J.
, 2015
, “Event-Triggered Fuzzy Filtering for a Class of Nonlinear Networked Control Systems
,” Signal Process.
, 113
, pp. 159
–168
.4.
Chadli
, M.
, Karimi
, H. R.
, and Shi
, P.
, 2014
, “On Stability and Stabilization of Singular Uncertain Takagi-Sugeno Fuzzy Systems
,” J. Franklin Inst.
, 351
(3
), pp. 1453
–1463
.5.
Chibani
, A.
, Chadli
, M.
, and Braiek
, N. B.
, 2016
, “A Finite Frequency Approach to Filtering for T-S Fuzzy Systems With Unknown Inputs
,” Asian J. Control.
, 18
(5
), pp. 1608
–1618
.6.
Kwon
, O. M.
, Park
, M. J.
, Park
, J. H.
, and Lee
, S.
, 2016
, “Stability and Stabilization of T-S Fuzzy Systems With Time-Varying Delays Via Augmented Lyapunov-Krasovskii Functionals
,” Inf. Sci.
, 372
, pp. 1
–15
.7.
Lee
, T. H.
, and Park
, J. H.
, 2017
, “New Methods of Fuzzy Sampled-Data Control for Stabilization of Chaotic Systems
,” IEEE Trans. Syst., Man, Cybern., Syst.
, PP
(99), pp. 1–9.8.
Liu
, Y.
, Guo
, B. Z.
, and Park
, J. H.
, 2017
, “Non-Fragile Filtering for Delayed Takagi-Sugeno Fuzzy Systems With Randomly Occurring Gain Variations
,” Fuzzy Sets Syst.
, 316
, pp. 99
–116
.9.
Liu
, Y.
, Park
, J. H.
, Guo
, B. Z.
, and Shu
, Y.
, 2017
, “Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control
,” IEEE Trans. Fuzzy Syst.
, PP
(99), p. 1.10.
Banu
, L. J.
, and Balasubramaniam
, P.
, 2014
, “Synchronisation of Discrete-Time Complex Networks With Randomly Occurring Uncertainties, Nonlinearities and Time-Delays
,” Int. J. Syst. Sci.
, 45
(7
), pp. 1427
–1450
.11.
Kwon
, O. M.
, Park
, M. J.
, Park
, J. H.
, Lee
, S.
, and Cha
, E. J.
, 2015
, “Improved Delay-Partitioning Approach to Robust Stability Analysis for Discrete-Time Systems With Time-Varying Delays and Randomly Occurring Parameter Uncertainties
,” Optim. Control Appl. Methods
, 36
(4
), pp. 496
–511
.12.
Sakthivel
, R.
, Aravindh
, D.
, Selvaraj
, P.
, Vimal Kumar
, S.
, and Marshal Anthoni
, S.
, 2017
, “Vibration Control of Structural Systems Via Robust Non-Fragile Sampled-Data Control Scheme
,” J. Franklin Inst.
, 354
(3
), pp. 1265
–1284
.13.
Su
, X.
, Shi
, P.
, Wu
, L.
, and Basin
, M. V.
, 2014
, “Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems
,” IEEE Trans. Cybern.
, 44
(12
), pp. 2470
–2483
.14.
He
, S.
, 2015
, “Energy-to-Peak Filtering for T-S Fuzzy Systems With Markovian Jumping: The Finite-Time Case
,” Neurocomputing
, 168
, pp. 348
–355
.15.
Hu
, J.
, Wang
, Z.
, Gao
, H.
, and Stergioulas
, L. K.
, 2012
, “Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities
,” IEEE Trans. Ind. Electron
, 59
(7
), pp. 3008
–3015
.16.
Hu
, J.
, Wang
, Z.
, Liang
, J.
, and Dong
, H.
, 2015
, “Event-Triggered Distributed State Estimation With Randomly Occurring Uncertainties and Nonlinearities Over Sensor Networks: A Delay-Fractioning Approach
,” J. Franklin Inst.
, 352
(9
), pp. 3750
–3763
.17.
Hu
, M.
, Guo
, L.
, Hu
, A.
, and Yang
, Y.
, 2015
, “Leader-Following Consensus of Linear Multi-Agent Systems With Randomly Occurring Nonlinearities and Uncertainties and Stochastic Disturbances
,” Neurocomputing
, 149
(Pt. B
), pp. 884
–890
.18.
Koo
, G. B.
, Park
, J. B.
, and Joo
, Y. H.
, 2017
, “Sampled-Data Fuzzy Filtering for Nonlinear Systems With Missing Measurements
,” Fuzzy Sets Syst.
, 316
, pp. 82
–98
.19.
Hao
, S.
, Lei
, S.
, and Park
, J. H.
, 2016
, “Extended Passive Filtering for Discrete-Time Singular Markov Jump Systems With Time-Varying Delays
,” Signal Process.
, 128
, pp. 68
–77
.20.
Shi
, P.
, Zhang
, Y.
, Chadli
, M.
, and Agarwal
, R. K.
, 2016
, “Mixed and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays
,” IEEE Trans. Neural Netw. Learn. Syst.
, 27
(4
), pp. 903
–909
.21.
Shen
, H.
, Park
, J. H.
, and Wu
, Z. G.
, 2015
, “Reliable Mixed Passive and Filtering for Semi-Markov Jump Systems With Randomly Occurring Uncertainties and Sensor Failures
,” Int. J. Robust Nonlin.
, 25
(17
), pp. 3231
–3251
.22.
Shu
, H.
, Yang
, H.
, Wang
, Z.
, Alsaadi
, F.
, and Hayat
, T.
, 2015
, “Almost Sure Filtering for Nonlinear Hybrid Stochastic Systems With Mode-Dependent Interval Delays
,” J. Franklin Inst.
, 352
(11
), pp. 4758
–4775
.23.
Wang
, S.
, Basin
, M. V.
, Zhang
, L.
, Zeng
, M.
, Hayat
, T.
, and Alsaedi
, A.
, 2016
, “Reliable Finite-Time Filtering for Impulsive Switched Linear Systems With Sensor Failures
,” Signal Process.
, 125
, pp. 134
–144
.24.
Yan
, H.
, Qian
, F.
, Yang
, F.
, and Shi
, H.
, 2016
, “ Filtering for Nonlinear Networked Systems With Randomly Occurring Distributed Delays, Missing Measurements and Sensor Saturation
,” Inf. Sci.
, 370–371
, pp. 772
–782
.25.
Sakthivel
, R.
, Sathishkumar
, M.
, Kaviarasan
, B.
, and Marshal Anthoni
, S.
, 2016
, “Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks With Markovian Jumping Parameters
,” Z. Naturforsch. A
, 71
(4
), pp. 289
–304
.26.
Sathishkumar
, M.
, Sakthivel
, R.
, Kwon
, O. M.
, and Kaviarasan
, B.
, 2017
, “Finite-Time Mixed and Passive Filtering for Takagi-Sugeno Fuzzy Nonhomogeneous Markovian Jump Systems
,” Int. J. Syst. Sci.
, 48
(7
), pp. 1416
–1427
.27.
Shen
, H.
, Li
, F.
, Wu
, Z.
, and Park
, J. H.
, 2016
, “Finite-Time Asynchronous Filtering for Discrete-Time Markov Jump Systems Over a Lossy Network
,” Int. J. Robust Nonlinear
, 26
(17
), pp. 3831
–3848
.28.
Shen
, M.
, Yan
, S.
, Zhang
, G.
, and Park
, J. H.
, 2016
, “Finite-Time Static Output Control of Markov Jump Systems With an Auxiliary Approach
,” Appl. Math. Comput.
, 273
, pp. 553
–561
.29.
Kwon
, O. M.
, Park
, M. J.
, Park
, J. H.
, Lee
, S.
, and Cha
, E. J.
, 2014
, “Improved Results on Stability of Linear Systems With Time-Varying Delays Via Wirtinger-Based Integral Inequality
,” J. Franklin Inst.
, 351
(12
), pp. 5386
–5398
.30.
Park
, M. J.
, Kwon
, O. M.
, Park
, J. H.
, Lee
, S. M.
, and Cha
, E. J.
, 2015
, “Stability of Time-Delay Systems Via Wirtinger-Based Double Integral Inequality
,” Automatica
, 55
, pp. 204
–208
.31.
Sakthivel
, R.
, Vimal Kumar
, S.
, Aravindh
, D.
, and Selvaraj
, P.
, 2016
, “Reliable Dissipative Sampled-Data Control for Uncertain Systems With Nonlinear Fault Input
,” ASME J. Comput. Nonlin. Dyn.
, 11
(4
), p. 041008.Copyright © 2018 by ASME
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