Feedback control and classification of generalized linear systems

Shayman, Mark A.; Zhou, Zheng

doi:10.1109/tac.1987.1104642

Cited by 57 publications

(23 citation statements)

References 25 publications

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“…Regularization of singular systems via state-feedbacks has been studied by different authors [10,23,27]. In general, those studies are based on the Weierstrass-Kronecker decomposition of the system, which uses two matrices P and Q that may change the information the original matrices.…”

Section: Introductionmentioning

confidence: 99%

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

Herrero

Ramı́rez

Thome

2014

Linear and Multilinear Algebra

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This paper deals with singular systems of index k ≥ 1. Our main goal is to find a state-feedback such that the closed-loop system satisfies the regularity condition and it is nonnegative and stable. In order to do that, the core-nilpotent decomposition of a square matrix is applied to the singular matrix of the system. Moreover, if the Drazin projector of this matrix is nonnegative then the previous decomposition allows us to write the core-part of the matrix in a specific block form. In addition, an algorithm to study this kind of systems via a state-feedback is designed.

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Section: Introductionmentioning

confidence: 99%

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

Herrero

Ramı́rez

Thome

2014

Linear and Multilinear Algebra

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“…where in (1) It is well known from classical control theory that derivative feedback is very essential for improving the stability and the performance of a control system (see e.g., [1][2][3]). In [1], PD controllers are employed to provide anticipatory action for overshoot reduction in the responses.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], PD controllers are employed to provide anticipatory action for overshoot reduction in the responses. In [2] and [3], PD controllers are used to achieve decoupling of linear systems. For descriptor systems, derivative feedback is even more important since it can alter many properties of a descriptor system, which a pure proportional state feedback can not.…”

Section: Introductionmentioning

confidence: 99%

“…For descriptor systems, derivative feedback is even more important since it can alter many properties of a descriptor system, which a pure proportional state feedback can not. Because of this reason, the use of PD control law in descriptor systems has been intensively and widely studied since the early 1980s [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Parametric eigenstructure assignment for descriptor systems via proportional plus derivative state feedback

Zhang

2011

Int. J. Control Autom. Syst.

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Eigenstructure assignment for descriptor systems with proportional plus derivative state feedback is studied. Based on a simple complete explicit parametric solution to a group of recursive equations, a parametric approach for eigenstrucure assignment in descriptor systems via proportional plus derivative state feedback is proposed. The proposed approach possesses the following features: 1) it does not impose any condition on the closed-loop eigenvalues, simultaneously assigns arbitrary n finite and infinite eigenvalues to the closed-loop system and guarantees the closed-loop regularity; 2) it is simple and needs less computational work; 3) it gives general complete parametric expressions for the closed-loop eigenvectors, the proportional state feedback gain matrix and the derivative state feedback gain matrix.

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“…La regularización de sistemas singulares a través de realimentaciones de estado fue estudiada por diferentes autores [38,40]. En general, estos trabajos se han basado en la descomposición de WeierstrassKronecker del sistema, la cual usa dos matrices P y Q que pueden cambiar la información de las matrices originales.…”

Section: Sistemas Singulares De Controlunclassified

Matrices no negativas y aplicaciones a sistemas singulares de control

Contrera¹,

Jorge²

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Feedback control and classification of generalized linear systems

Cited by 57 publications

References 25 publications

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

Parametric eigenstructure assignment for descriptor systems via proportional plus derivative state feedback

Matrices no negativas y aplicaciones a sistemas singulares de control

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