On eigenstructure assignment using block poles placement

Yaici, Malika; Hariche, Kamel

doi:10.1016/j.ejcon.2014.05.003

Cited by 19 publications

(14 citation statements)

References 28 publications

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“…As for an eigenvalue system, a block Vandermonde matrix can be defined for solvents with particular properties [15].…”

Section: Block Vandermonde Matricesmentioning

confidence: 99%

“…Block Vandermonde matrices constructed using matrix polynomials solvents are very useful in control engineering, for example in control of multi-variable dynamic systems described in matrix fractions (see [15]). It is in these particular BVM that we are interested.…”

Section: Introductionmentioning

confidence: 99%

“…The non-trivial vector v i , solution of the equation A(λ i )v i = 0, is called a primary right latent vector associated to the latent value λ i . Similarly, the non trivial row vector w, solution of the equation wA(λ i ) = 0 is called a primary left latent vector associated with λ i[15].…”

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confidence: 99%

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A particular block Vandermonde matrix

Yaici

Hariche

2019

ITM Web Conf.

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The Vandermonde matrix is ubiquitous in mathematics and engineering. Both the Vandermonde matrix and its inverse are often encountered in control theory, in the derivation of numerical formulas, and in systems theory. In some cases block vandermonde matrices are used. Block Vandermonde matrices, considered in this paper, are constructed from a full set of solvents of a corresponding matrix polynomial. These solvents represent block poles and block zeros of a linear multivariable dynamical time-invariant system described in matrix fractions. Control techniques of such systems deal with the inverse or determinant of block vandermonde matrices. Methods to compute the inverse of a block vandermonde matrix have not been studied but the inversion of block matrices (or partitioned matrices) is very well studied. In this paper, properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. A parallelization of these algorithms is also presented. The proposed algorithms are validated by a comparison based on algorithmic complexity.

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“…As for an eigenvalue system, a block Vandermonde matrix can be defined for solvents with particular properties [15].…”

Section: Block Vandermonde Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A particular block Vandermonde matrix

Yaici

Hariche

2019

ITM Web Conf.

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“…Robust performance is defined as the low sensitivity of system performance with respect to system model uncertainty and terminal disturbance. It is well known that the eigenvalues of the dynamic matrix determine the performance of the system then from that the sensitivities of these eigenvalues determine the robustness of the system (2).…”

Section: The Sensitivity Of Eigenvalues (Robust Performance)mentioning

confidence: 99%

“…So its sensitivity to uncertainties is very important when analyzing and designing the system. Stability is affected by the system eigenvalues of the dynamic matrix so the sensitivity of these eigenvalues directly affects the robust stability of the system (2). There are three robust stability measures using the sensitivity of this system eigenvalues defined as follows:…”

Section: Robust Stabilitymentioning

confidence: 99%