Fault detection for fractional‐order linear systems in finite frequency domains

Sensor fault detection for dynamic point‐the‐bit rotary steerable system via finite‐frequency domain observer and zonotope residual evaluation

“…The condition can be easily proved by pre-and postmultiplying (34) with [I  T ] and [I  T ] T . Since T ΔA(k) follows Assumption 3.1, the inequation (34) can be rewritten as:…”

“…Note that since faults usually emerge in a specified range, designing a finite-frequency range FDO has proven helpful in reducing conservativeness [30][31][32]. Recently, based on the generalized Kalman-Yakubovich-Popv (GKYP) Lemma [33], the finite frequency range H ∞ and H − ∕H ∞ optimization problems have been formulated for many applications [11,32,34,35], for instance, in the presence of unknown inputs, the state estimation problem [35] and the fault detection filter design problem [32] have been studied for the T-S systems. It should be pointed out that since the DPRSS operates in a harsh drilling environment, parameter uncertainties, neglected dynamics, measurement disturbances, and unknown inputs are inevitable.…”

“…Compared with the existing full-frequency FD approaches in [12,18,[27][28][29], the proposed FDO is less conservative because it concerns the middle-frequency rang domain. Furthermore, unlike the finite frequency domain FDOs designed in [11,[30][31][32]34], the proposed FDO can detect sensor faults subject to parameter uncertainties, neglected model dynamics, measurement disturbances, and unknown inputs with large amplitude. (iii) A residual evaluation method is proposed by constructing residual bounds based on zonotope, and an FD decision logic is presented.…”

Event‐triggered fault detection for discrete‐time Markovian jump systems in finite frequency domain

“…[21][22][23] However, all the aforementioned papers are devoted to designing FD methods for MJ systems in full frequency domain. In fact, the fault signal existing in the actual physical system usually has a specific frequency domain, 24 which is ignored in References 21-23. Luckily, generalized Kalman-Yakubovich-Popov (GKYP) lemma opens the door for the investigation of finite frequency FD problems by transforming various performances in finite frequency interval into feasible linear matrix inequality (LMI) conditions.…”