Fault Detection Finite-Time Filter Design for T–S Fuzzy Markovian Jump System with Missing Measurements

• Published in: Circuits, systems, and signal processing Vol. 40; no. 4; pp. 1607 - 1634
• Main Authors: Sakthivel, R., Suveetha, V. T., Divya, H.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2021; Springer Nature B.V
• Subjects: Circuits and Systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Fault detection; Filter design (mathematics); Fuzzy systems; Instrumentation; Signal,Image and Speech Processing; Transition probabilities; White noise; T–S fuzzy Markovian jump system; Fault detection filter design; Missing measurements; Stochastic finite-time boundedness; Randomly occurring uncertainties
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-020-01552-1

The primary purpose of this work was to address the problem of finite-time fault detection filtering for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markovian jump systems subject to randomly occurring uncertainties, time-varying delay, missing measurements and partly unknown transition probability matrices. Precisely the missing measurement phenomenon in the network environment satisfies the Bernoulli distributed white noise sequences. Firstly a fuzzy rule-dependent filter is constructed for estimating the unmeasured states of the system and the corresponding fault detection problem. Further, based on the filtering problem, the error between residual and fault is minimized with the prescribed strict ( Q , S , R ) - γ dissipativity performance. Secondly, the sufficient criteria are derived to ensure the filtering error system to be finite-time stochastic bounded. Finally, the applicability and usefulness of the proposed filter design through two numerical examples are verified.