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The paper outlines a new approach to the signal reconstruction process in multivariable wireless communications tasks. A new solution is proposed using the so-called Smith factorization, which is efficiently used in the synthesis of control systems described by polynomial matrix notation. In particular, the so-called polynomial S-inverse is used, which, together with the applied degrees of freedom,...
In this paper a breakthrough in the area of the minimum-energy perfect control for discrete-time state-space systems with different number of input and output variables is presented. Following the recently performed heuristic simulation studies corresponding to mentioned control strategy, the analytical confirmation is presented through this paper. Up to now, the statement that the so-called right...
The paper presents an approach to the synthesis of MV control systems with respect to minimum-energy of the control inputs. Due to the reason, a recently introduced polynomial matrix σ-inverse is applied to LTI nonsquare systems described by discrete-time state-space framework. It is shown that classical minimum-norm right inverse is not sufficient to obtain the minimum-energy of control runs. Thus,...
In this paper a new SVD-based inverse of nonsquare parameter matrices is presented. An intriguing impact of H-inverse on minimum-energy design of perfect control inputs is emphasized. Now, the new inverse corresponds to the polynomial matrix S-inverse introduced by Hunek and Latawiec for systems described in the input-output framework. Note that the new inverse can be extended to cover the polynomial...
The paper concerns some studies on effectiveness of nonsquare matrix σ-inverse and T-inverse methods to the synthesis of minimum-energy fault-tolerant control for discrete-time LTI MIMO systems. The proposed method has noted that in the transient states, σ-inverse is more effective than the generally known Moore-Penrose approach. The effectiveness is expressed in terms of minimum-energy for the perfect...
In this paper reconstructing method of spherical and variable in time surface based on estimation of the instantaneous values phase with imaginary part of complex white light interferogram logarithm is presented. An accuracy analysis of the above-mentioned method in terms of reconstruction of spherical surface is done here. The methodology of research concerns the synthesis of surface through the...
In this paper an useful application of a new right H-inverse to stabilization of perfect control for LTI MIMO discrete-time systems in state-space is shown. Following the recently introduced H-inverse, its intriguing property giving the stable perfect control is indicated here. Now, the SVD-based H-inverse with parameter and polynomial degrees of freedom clearly outperforms the classical minimum-norm...
In this paper a concept of application of polynomial matrix σ-inverse in multivariable state-space perfect control is presented. The new inverse is derived from perfect control of systems described by the input-output approach. Rather surprisingly, the σ-inverse clearly outperforms some other inverses of nonsquare parameter matrices, including the classical minimumnorm right one. A minimum-energy...
In this paper, a new definition of a right inverse of nonsquare parameter matrices is derived from MVC-related inverses of nonsquare polynomial matrices. The new definition is employed in a stabilizing state-space perfect control law for nonsquare LTI MIMO systems. A simulation example shows that the new inverse outperforms the classical minimum-norm right inverse.
This paper presents a new concept of modeling of LTI SISO discrete-time fractional-order systems, in which the Laguerre filters are employed to model both 1) the Grünwald-Letnikov fractional difference and 2) a dynamics of the LTI SISO fractional-order system. Such a ‘double-Laguerre’ concept yields original accuracy and computational results at both modeling stages, illustrated with a series of simulation...
Normalized finite fractional differences are considered as an approximation to the Grunwald-Letnikov fractional difference. In particular, adaptive finite fractional difference (AFFD) is recalled and effectively modified by the introduction of a time-varying forgetting factor. The modified AFFD is shown in simulations to provide an excellent approximation performance, both in terms of the modeling...
This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.
This paper presents (structurally stable) pole-free control designs for (a deterministic version of) generalized minimum variance control and linear quadratic regulation for nonsquare LTI MIMO systems. For both discrete-time control strategies, two alternative approaches are offered, the numerical one related with limiting control solutions as control weighting matrices tend to the zero ones and the...
Constrained minimum variance control is offered for nonsquare LTI MIMO systems. A constrained control design takes advantage of the so-called control zeros. The new control strategy is compared with familiar generalized minimum variance control and possible application areas of the two are discussed.
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