Inner-outer factorizations of right-invertible real-rational matrices

Yen, Fang-Bo; Wei, Lin-Fang

doi:10.1016/0167-6911(90)90077-8

Cited by 17 publications

(6 citation statements)

References 5 publications

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“…It is not difficult to show that both v and w are the so-called minimal-phase inner functions without any transmission zeros in the left-half plane 20 and with compatible dimensions, respectively. It is easy to yield that whereas (with Q ' 6…”

Section: Design Proceduresmentioning

confidence: 99%

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Refined H-infinity-optimal approach to rotorcraft flight control

Young

Lin

1993

Journal of Guidance, Control, and Dynamics

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This paper introduces an approach to refine the //°°-optimal controller for the four-block H°° control problem. The second singular value of the compensated system can be analyzed and synthesized with a free parameter by the proposed approach. This approach is implementable in computation with an appropriate selection of a diagonalizing matrix pair. The H°° norm of the sublayers can, therefore, be improved. The characterization of the sublayers for the four-block problem is also completed. The problems that required higher robustness are suggested by this proposed approach. Furthermore, an engineering application concerning the rotorcraft flight control is provided. The simulation results bestow a promising progress both in the frequency domain and in the time domain. The gain margin, phase margin, settling time, and damping effect are improved in this example.

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Section: Design Proceduresmentioning

confidence: 99%

“…inf || | T(s)_S(s) whereas K stabilizes the plant G internally. From Eq (20). and by coprime factorization, the equivalent distance problem in…”

mentioning

confidence: 99%

Refined H-infinity-optimal approach to rotorcraft flight control

Young

Lin

1993

Journal of Guidance, Control, and Dynamics

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“…An inner system is not minimum-phase if PQ I − is not positive definite where P and Q are the controllability grammian and the observability grammian of this inner system, respectively [21].…”

Section: Problem: the Best Optimal Hankel-nrom Approximationmentioning

confidence: 99%

The best optimal Hankel-norm approximation of railway active wheelset models

Young

2010

Proceedings of the 2010 American Control Conference

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This paper presents an application of the model reduction for the wheelset of the railway vehicle from the best optimal Hankel-norm approximation. It is necessary to reduce the complexity of the control synthesis by model reduction techniques since the wheelset model is highly interactive with high order. The proposed approach solves the best optimal solution layer by layer from any optimal solution of each layer. This approach adopts the left inverses of inner function vectors characterized from the Schmidt pair. The McMillan degree of the reduced-order model for the successive layer can be determined. Fuerthermore, this successive layer will also become another approximation problem. This paper also proposes an algorithm to calculate the best optimal approximation recursively. The best optimal Hankel-norm approximation will be compared with the other optimal Hankel-norm approximation in frequency domain for the transfer function matrix and all its arrays. The results reveal that the best optimal Hankel-norm approximation is better in sense of the singular values not only in all layers but in all arrays.

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“…For instance, in [4] the factors were derived by considering G * G + ε 2 I , and deducing the outer factor from this by solving a reduced Riccati equation. In [21] the reduced Riccati equation is replaced by a different approach, avoiding in fact an approximation procedure. In that paper, first the inner-outer factorization for G(s) * is computed, and then balanced coordinates are used to further factor the inner part of G(s) * .…”

Section: Introductionmentioning

confidence: 99%

“…Finally, it is emphasized that the previous methods to compute the inner-outer factorization rely mainly on state space methods. Roughly speaking, the previous methods involve solving Riccati equations, Hamilton methods, decomposing the state space with balanced coordinates or other decompositions, or eigenvectors and eigenvalues for certain state space operators; see for instance [4,16,17,21]. Our approach is quite different.…”

Section: Introductionmentioning

confidence: 99%

Inner Outer Factorization of Wide Rational Matrix Valued Functions on the Half Plane

Frazho

Ran

2021

Operator Theory, Functional Analysis and Applications

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Inner-outer factorizations of right-invertible real-rational matrices

Cited by 17 publications

References 5 publications

Refined H-infinity-optimal approach to rotorcraft flight control

Refined H-infinity-optimal approach to rotorcraft flight control

The best optimal Hankel-norm approximation of railway active wheelset models

Inner Outer Factorization of Wide Rational Matrix Valued Functions on the Half Plane

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