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“…The mapping E : R nz → R n E is a static algebraic mapping capturing the nonlinearity of the dynamics. Let n r represent the number of rows in (1), and the matrices H(q), L(q), F (q) are polynomial functions with n r rows and n x , n z , n f columns in the variable q, which represents the shift operator. As such, these matrices may be cast as linear operators in the space of discrete-time signals.…”

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“…The mapping E : R nz → R n E is a static algebraic mapping capturing the nonlinearity of the dynamics. Let n r represent the number of rows in (1), and the matrices H(q), L(q), F (q) are polynomial functions with n r rows and n x , n z , n f columns in the variable q, which represents the shift operator. As such, these matrices may be cast as linear operators in the space of discrete-time signals.…”

“…This methodology is found in a great variety of model-settings, e.g., from single non-linear systems [8] towards multi-agent, possibly large scale, systems [19,5,6]. A more integral approach for detection and isolation of faults is an unknowninput type estimator, which decouples the effect of unknown state measurements and disturbances (or faults) from the residual through an algebraic approach [16,9] or approaches using the generalized inverse [1,27]. Multiplicative faults are inherently more difficult to detect and isolate due to their non-linear appearance in the model, hence, it requires non-linear approaches, e.g., adaptive-type observers [23] or sliding-mode observers [21].…”

“…The iterative/recursive algorithms are the typical parameter identification algorithms [9], which have a wide range of applications in seeking the roots of the equation and developing parameter estimation methods [10][11][12][13][14]. Ansari and Bernstein proposed the deadbeat unknown-input state estimation and input reconstruction for linear discrete-time systems [15]; Xu et al presented a hierarchical Newton and least squares iterative estimation algorithm for dynamic systems based on the impulse responses [16]. Recently, Xia et al presented an improved least-squares identification for multiple-output non- linear stochastic systems [17].…”

“…Identification of the state‐space systems has received considerable attention in the past few decades [24–26]. There are various identification methods, representatively such as the subspace identification algorithm, the recursive least‐squares algorithm, and the Kalman filter algorithm [27].…”