Research Papers

Finite Time Passive Reliable Filtering for Fuzzy Systems With Missing Measurements

[+] Author and Article Information
S. Vimal Kumar

Department of Mathematics,
Anna University,
Regional Campus,
Coimbatore 641046, India
e-mail: svimalkumar16@gmail.com

R. Sakthivel

Department of Mathematics,
Sungkyunkwan University,
Suwon 440-746, South Korea
e-mail: krsakthivel@yahoo.com

M. Sathishkumar

Department of Mathematics,
Anna University,
Regional Campus,
Coimbatore 641046, India
e-mail: sathishmaths21@gmail.com

S. Marshal Anthoni

Department of Mathematics,
Anna University,
Regional Campus,
Coimbatore 641046, India
e-mail: smarshalanthoni@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 9, 2017; final manuscript received November 18, 2017; published online March 13, 2018. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(8), 081009 (Mar 13, 2018) (10 pages) Paper No: DS-17-1143; doi: 10.1115/1.4039183 History: Received March 09, 2017; Revised November 18, 2017

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.

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Grahic Jump Location
Fig. 1

Block diagram of T–S fuzzy filtering error system

Grahic Jump Location
Fig. 2

The trajectories of state and its estimation: (a) state x1 and its estimation x̂1 and (b) state x2 and its estimation x̂2

Grahic Jump Location
Fig. 3

Membership function and filtering error: (a) membership function and (b) filter error

Grahic Jump Location
Fig. 4

E{xT(t)Rx(t)} and bound of c2: (a) Time history of E{xT(t)Rx(t)} and (b) the optimal bound of c2 with different values of η

Grahic Jump Location
Fig. 6

E{xT(t)Rx(t)} and filter error (a) time history of E{xT(t)Rx(t)} and (b) filter error

Grahic Jump Location
Fig. 5

The trajectories of state and its estimation: (a) state x1 and its estimation x̂1 and (b) state x2 and its estimation x̂2



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