Robust pole assignment via Sylvester equation based state feedback parametrization

Varga, A.

doi:10.1109/cacsd.2000.900179

Cited by 70 publications

(84 citation statements)

References 17 publications

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“…The Sylvester realizations R k , given the pivot matrix A and feedback matrix F, are all unique by construction. For the choice of A we can take a block-diagonal or block-Jordan matrix [14] which never shares eigenvalues with any of the A k matrices. This can be accomplished by choosing the eigenvalues of A close to the imaginary axis (see also the numerical simulations).…”

Section: Uniform Approach By Sylvester Equationsmentioning

confidence: 99%

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

Samuel

Knockaert

Dhaene

2014

Informatics in Control, Automation and Robotics

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Abstract. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. The direct parameterization of poles and residues may be not appropriate, due to their possible nonsmooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the a pole-residue description to a Sylvester description which is computed for each root macromodel.This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester technique for parametric macromodeling.

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Section: Uniform Approach By Sylvester Equationsmentioning

confidence: 99%

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

Samuel

Knockaert

Dhaene

2014

Informatics in Control, Automation and Robotics

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“…The matrix (18) requires the identification of , which can be computed using the technique proposed in [23]. Another interesting approach based on the solution of a Sylvester equation can be found in [24]. Some assumptions concerning observability and controllability must be satisfied for these approaches and for the uniqueness of the solution [23], [24].…”

Section: ) Pole Placement Approachmentioning

confidence: 99%

“…Another interesting approach based on the solution of a Sylvester equation can be found in [24]. Some assumptions concerning observability and controllability must be satisfied for these approaches and for the uniqueness of the solution [23], [24]. The matrix is used to place the eigenvalues of the matrix and, therefore, the poles of the root macromodels in such a way that they are equal to .…”

Section: ) Pole Placement Approachmentioning

confidence: 99%

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Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

Samuel

Knockaert

Ferranti

et al. 2013

IEEE Trans. Microwave Theory Techn.

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Abstract-A novel state-space realization for parameterized macromodeling is proposed in this paper. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. This technique is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parameterized macromodels. The key points of the novel state-space realizations are the choice of a proper pivot matrix and a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester realization for parameterized macromodeling.

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“…There exist a few papers on robustness for the complete eigenvalue assignment in the first-order control systems, such as those, by Keel et al [26], Keel and Bhattacharyya [25], Cavin III and Bhattacharyya [7], Varga [39,40], etc. However, work on robustness for quadratic partial eigenvalue assignment is rare.…”

Section: Q2mentioning

confidence: 99%

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

Bai

Datta

Wang

2010

Mechanical Systems and Signal Processing

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a b s t r a c tThe partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spillover). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant ''no spill-over property'' of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations.& 2009 Published by Elsevier Ltd.

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Robust pole assignment via Sylvester equation based state feedback parametrization

Cited by 70 publications

References 17 publications

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

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