Linear Discrete-Time Systems

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“…The optimisation is made in the parameter space of three unknown and adjustable parameters, unlike the classical optimisation which was done in the parameter plane of two parameters. The procedure is based on the solution [27,29] of the major controversies between the classical transfer function matrix and the system stability investigation using this matrix. This controversy has been recently solved by developing and introducing the full transfer function matrix [27,29] so that during the system conditional optimisation the characteristic polynomial of the full transfer function matrix is used and not of the classical transfer function.…”

“…Equation ( 1) is generated through the Lyapunov's coordinate transformation process, that is, y = Y-Y d is the plant output deviation from the desired output Y d , and u P =U P -U PN is the plant input deviation from the nominal input U PN . The compact form of Equation ( 1) is as follows [27,28,29]:…”

“…The proposed optimisation procedure is completely new. The full block diagram [27] of the system is shown in Fig. 1.…”

“…The transfer function is defined for the system in the forced working regime under non-zero input and all zero initial conditions. This controversy has been recently solved by introducing and developing the full transfer function matrix [27,28,29]. The conditional optimisation synthesis procedure is carried out herein by using the characteristic polynomial of the full transfer function matrix and not of the classical one.…”

Online Deconvolution for Industrial Hyperspectral Imaging Systems

“…Let D be the closed unit disc in the complex plane. We say that the matrix A is discrete stable (see [6]) if δ(z) = det(I − zA) = 0, ∀z ∈ D. Using the Schur determinant formula, it can be shown that:…”