Eigenstructure assignment in descriptor systems

Fletcher, L. R.; Kautský, Jaroslav; Nichols, Nancy K.

doi:10.1109/tac.1986.1104189

Cited by 107 publications

(52 citation statements)

References 8 publications

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“…For given matrices A, C ∈ R p×n , B, D ∈ R n×q , E ∈ R p×q , and P ∈ SOR n×n , find the generalized centro-symmetric matrix Y ∈ CSR n×n P , such that The matrix equation AYB+CY T D = E plays important roles in the system theory, such as eigenstructure assignment [6], observer design [7], control of system with input constraint [8], and fault detection [9].…”

Section: Problem 13mentioning

confidence: 99%

The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

Hajarian

Dehghan

2011

Math. Meth. Appl. Sci.

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An n×n real matrix P is said to be a symmetric orthogonal matrix if P = P −1 = P T . An n×n real matrix Y is called a generalized centro-symmetric with respect to P, if Y = PYP. It is obvious that every matrix is also a generalized centrosymmetric matrix with respect to I. In this work by extending the conjugate gradient approach, two iterative methods are proposed for solving the linear matrix equation

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Section: Problem 13mentioning

confidence: 99%

The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

Hajarian

Dehghan

2011

Math. Meth. Appl. Sci.

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“….a, q 3 Step W: Select matrix W to minimize B [E + ASWS t+ 8wsT1B subject to BE + AS.SI + BWSTI S tol , where tol is some given tolerance.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

“…These algorithms are based on the procedures developed in (5] (E) are shown in [3] and [4] to be given by:…”

Section: Introductionmentioning

confidence: 99%

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Algorithms for Robust Pole Assignment in Singular Systems

Kautský

Nichols

1986

1986 American Control Conference

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“…plays important roles in system theory, such as eigenstructure assignment [29], observer design [4], control of system with input constraint [28], and fault detection [30].…”

Section: Introductionmentioning

confidence: 99%

Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

Dehghan

Hajarian

2012

Comput. Appl. Math.

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Abstract. An n × n real matrix P is said to be a generalized reflection matrix if P T = P and P 2 = I (where P T is the transpose of P). A matrix A ∈ R n×n is said to be a reflexive (antireflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = −P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equationsover reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms.Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.

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Eigenstructure assignment in descriptor systems

Cited by 107 publications

References 8 publications

The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

Algorithms for Robust Pole Assignment in Singular Systems

Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

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