Annulus-Event-Based Finite-Time Fault Detection for Discrete-Time Nonlinear Systems with Probabilistic Interval Delay and Randomly Occurring Faults

• Published in: Circuits, systems, and signal processing Vol. 41; no. 9; pp. 4818 - 4847
• Main Authors: Wu, Zhihui, Li, Bei, Hu, Jun, Chen, Dongyan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2022; Springer Nature B.V
• Subjects: Annuli; Circuits and Systems; Communication; Design; Discrete time systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Fault detection; Instrumentation; Linear matrix inequalities; Markov analysis; Markov chains; Mathematical analysis; Nonlinear systems; Performance indices; Probability theory; Random variables; Science; Signal processing; Signal,Image and Speech Processing; Statistical analysis; Time lag; Randomly occurring faults; Finite-time stability; Event-triggered mechanism; Fault detection; Time-varying delay; Discrete nonlinear system
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-022-02019-1

In this paper, the finite-time fault detection (FTFD) problem is investigated for a class of discrete-time nonlinear systems subject to the probabilistic interval time-varying delay and the randomly occurring faults (ROFs) under the annulus-event-based communication strategy (AEBCS). A Bernoulli stochastic variable is used to depict the probability interval time-varying delay phenomenon, where the time delay is bounded and its probability distributions can be observed. The phenomena of the ROFs are characterized by the Markov chain with two states. Furthermore, the AEBCS is applied to determine whether the measured signals can be transmitted to the filter or not. For the fault detection (FD) problem, we propose some sufficient conditions to ensure that the error dynamics system is finite-time stochastically stable with the specified H ∞ performance index. Meanwhile, the gains of the filter can be calculated via the feasible solution to certain linear matrix inequalities. In the end, two numerical examples are proposed to verify the effectiveness of newly proposed FTFD method via the AEBCS.