Partial eigenvalue assignment problem of high order control systems using orthogonality relations

Ramadan, Mohamed A.; El-Sayed, Ehab A.

doi:10.1016/j.camwa.2009.07.063

Cited by 22 publications

(22 citation statements)

References 8 publications

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“…The approach needs the knowledge of only a few eigenvalues and with corresponding left eigenvectors of matrix polynomial P(λ) without turning high order systems into first order form. When τ = 0 is a special case of our results see the reference (Ramadan and El-Sayed, 2010).…”

Section: Resultsmentioning

confidence: 69%

“…Consider high order dynamical system (Duan, 2005;Dedieu and Tisseur, 2003;Dedieu and Tisseur, 2001) of the form: Is very often referred to as λ matrix, or matrix polynomial of degree k (Dedieu and Tisseur, 2003;Dedieu and Tisseur, 2001;Wang and Zhang, 2013;Ramadan and El-Sayed, 2010). lambda (λ) is the characteristic roots of Equation (1.3), i.e., det(P(λ)) = 0, are known as eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

“…The vectors y ≠ 0 and x ≠ 0 are corresponding left and right eigenvectors respectively which satisfy y H P(λ) = 0 and P(λ)x = 0, where H is the conjugate transpose. The standard eigenvalue problem Ax = λx is the special case of (1.2) for example, the references Wang and Zhang, 2013;Ramadan and El-Sayed, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…PEAP for high-order linear systems without time delay introduced in many paper (Wang and Zhang, 2014;Ramadan and El-Sayed, 2010). Prattand and Singh (2009) were solution PEAP for second order linear system with known time delay in single-input case.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Partial Eigenvalue Assignment for High-Order Linear Systems in a Time Delayed System

El-Sayed¹,

Behady²

2016

American Journal of Applied Sciences

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This paper introduces a solution to the partial eigenvalues assignment problem of high order linear systems with time delayed system in both single-input and multi-input cases using orthogonality relations between eigenvectors of the matrix polynomial. The solution requires the knowledge of only a few eigenvalues and with corresponding left eigenvectors of matrix polynomial. The numerical examples are done to illustrate the proposed method.

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Section: Resultsmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Partial Eigenvalue Assignment for High-Order Linear Systems in a Time Delayed System

El-Sayed¹,

Behady²

2016

American Journal of Applied Sciences

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“…A survey on the entire eigenstructure method has been conducted by [5], and used by [6] for control system design. An algorithmic approach to eigenvalue assignment has been conducted by [7], besides, partial assignment using orthogonality relations by [8]. In addition, studies regarding existence, uniqueness, and numerical solution have been conducted by [9].…”

Section: Introductionmentioning

confidence: 99%

Explicit Determination of State Feedback Matrices

El-Ghezawi¹

2015

APM

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Methods which calculate state feedback matrices explicitly for uncontrollable systems are considered in this paper. They are based on the well-known method of the entire eigenstructure assignment. The use of a particular similarity transformation exposes certain intrinsic properties of the closed loop w-eigenvectors together with their companion z-vectors. The methods are extended further to deal with multi-input control systems. Existence of eigenvectors solution is established. A differentiation property of the z-vectors is proved for the repeated eigenvalues assignment case. Two examples are worked out in detail.

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An algorithm of partial eigenstructure assignment for high‐order systems

Zhang

Wang

2018

Math Methods in App Sciences

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We put forward an algorithm for the issue on the partial eigenstructure assignment in a high-order system, in which some certain eigenpairs, in a given system, can be assigned without changing others. Then a differential equation could be used to model the given systems, so that a multi-input state feedback control deal with this assignment. Moreover, the algorithm requests the information of a few of the eigenpairs merely. As well some numerical cases are shown to prove the effect of our algorithm. KEYWORDShigh-order systems, partial eigenvalue assignment, state feedback controlThe characteristic roots of the polynomial equation (3), namely, det[P K ( )] = 0, are known as eigenvalues. Vectors z ≠ 0 and x ≠ 0 are the corresponding left and right eigenvectors, ie, z H P K ( ) = 0, P K ( )x = 0,where H denotes the conjugate transpose.

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Partial eigenvalue assignment problem of high order control systems using orthogonality relations

Cited by 22 publications

References 8 publications

Partial Eigenvalue Assignment for High-Order Linear Systems in a Time Delayed System

Partial Eigenvalue Assignment for High-Order Linear Systems in a Time Delayed System

Explicit Determination of State Feedback Matrices

An algorithm of partial eigenstructure assignment for high‐order systems

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