Input–output method to fault detection for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses

Distributed H∞ Consensus Fault Detection for Uncertain T‐S Fuzzy Systems with Time‐Varying Delays Over Lossy Sensor Networks

“…to denote the relation  2 from d (k) to d (k) in (16). The following lemma shows that the l 2 induced norm of Δ d is bounded by one.…”

“…Consequently, a fault detection technology is needed to monitor the system behaviour by indicating the occurrence, location and size of the fault. Over the past decades, fruitful results regarding fault detection have been obtained [10][11][12][13][14][15][16][17][18][19]. However, most of these results on fault detection focus on the centralised architecture, which may not be suitable to distributed sensor networks.…”

“…One such challenge is the network-induced packet-dropout phenomenon that has recently drawn considerable research attention. Various approaches have been presented in the literature to model the packet dropout phenomenon [6][7][8][9], [13][14][15][16][17]. It should be pointed out that, almost all the literature concerning packet-dropout phenomenon have been specifically considered for networked control systems (NCSs) [16,17,25].…”

The design of reliable adaptive controllers for time-varying delayed systems based on improved H∞ performance indexes

“…Research on time-varying delayed systems [5][6][7][8] is a recurring subject due to its practical and theoretical significance. The main methods of the research on time-varying delayed systems can be classified into two types: delay-independent type [9,10] and delay-dependent type [11,12].…”

“…In Theorem 2, sufficient conditions for the existence of the adaptive reliable controller(8) which is composed of constant controller gains and and time varying parameters updated online according to the adaptive law(16) are given in terms of solutions to a set of LMIs (26)-(29). However, it should be pointed out that the LMIs involved in (26)-(29) could be complex, which may make the computation costly for the system with a higher dimension and more actuator fault modes.…”