On Solvents of Matrix Polynomials

Yaici, Malika; Hariche, Kamel

doi:10.7763/ijmo.2014.v4.385

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…The right matrix fraction description (RMFD) [24][25][26] of the system can be formulated directly from (11-a) as, ( ) = ( ) −1 ( )…”

Section: Feedback Linearizationmentioning

confidence: 99%

“…It is known that if a linear-time-invariant MIMO system described by a state space equation has a number of states divisible by the number of inputs and it can be transformed to block controller form, we can design a state feedback controller using block pole placement technique by assigning a set of desired Block poles. These may be left or right block poles [23][24][25][26]. The eigenvalues and eigenvectors (eigenstructure) of the state matrix can determine system performance and robustness more directly and explicitly than other indicators.…”

Section: Introductionmentioning

confidence: 99%

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State feedback linearization using block companion similarity transformation

et al. 2021

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In this research work, a new method is proposed for linearizing a class of nonlinear multivariable system; where the number of inputs divides exactly the number of states. The idea of proposed method consists in representing the original nonlinear system into a state-dependent coefficient form and applying block similarity transformations that allow getting the linearized system in block companion form. Because the linearized system’s eigenstructure can determine system performance and robustness far more directly and explicitly than other indicators, the given class multivariable system is chosen. Examples are used to illustrate the application and show the effectiveness of the given approach.

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“…The right matrix fraction description (RMFD) [24][25][26] of the system can be formulated directly from (11-a) as, ( ) = ( ) −1 ( )…”

Section: Feedback Linearizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

State feedback linearization using block companion similarity transformation

et al. 2021

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“…where:N R , D R , N L andD L are matrix polynomials and λ stands for the d dt operator. see [[4]],[ [40]] and [ [48]] and the reference therein . The obtained λmatrix transfer function of the power plant gas turbine system is: We try to decouple the power plant turbine dynamic model.…”

Section: Application In Control Engineeringmentioning

confidence: 99%

On The Block Decomposition and Spectral Factors of λ-Matrices

Bekhiti,

Dahimene,

Hariche

et al. 2018

Preprint

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In this paper we factorize matrix polynomials into a complete set of spectral factors using a new design algorithm and we provide a complete set of block roots (solvents). The procedure is an extension of the (scalar) Horner method for the computation of the block roots of matrix polynomials. The Block-Horner method brings an iterative nature, faster convergence, nested programmable scheme, needless of any prior knowledge of the matrix polynomial. In order to avoid the initial guess method we proposed a combination of two computational procedures . First we start giving the right Block-Q. D. (Quotient Difference) algorithm for spectral decomposition and matrix polynomial factorization. Then the construction of new block Horner algorithm for extracting the complete set of spectral factors is given.

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“…The conditions for the existence and uniqueness of the complete set of solvents have been investigated by P. Lancaster [15] and Malika Yaici [3].…”

Section: Latent Root and Latent Vectormentioning

confidence: 99%

“…The design of state feedback control in MIMO systems leads to the so-called matrix polynomials assignment [2]. The use of block poles constructed from a desired set of closed-loop poles offers the advantage of assigning a characteristic matrix polynomial rather than a scalar one [3]. The desired characteristic matrix polynomial is first constructed from a set of block poles selected among a class of similar matrices, and then the state feedback is synthesized by solving matrix equations.…”

Section: Introductionmentioning

confidence: 99%