Elementary Proof of Controller Parametrization Without Coprime Factorizability

Mori, Kazuyoshi

doi:10.1109/tac.2004.825618

Cited by 19 publications

(14 citation statements)

References 24 publications

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“…Then the results of [33,37] can be used in order to see how restrictive it is to assume existence of both coprime factorizations from the theoretical point of view. Secondly, one can use the stabilization theory based on general factorization developed by Mori [25] and Quadrat [34] to develop robust regulation theory without using coprime factorizations. This is a promising direction of research since the problem formulation of this article would allow the use of the algebraic results presented in [25,34].…”

Section: Concluding Discussion and Directions For Future Researchmentioning

confidence: 99%

“…Secondly, one can use the stabilization theory based on general factorization developed by Mori [25] and Quadrat [34] to develop robust regulation theory without using coprime factorizations. This is a promising direction of research since the problem formulation of this article would allow the use of the algebraic results presented in [25,34]. The results obtained would make the theory more applicable and general since no coprime factorizations are needed.…”

Section: Concluding Discussion and Directions For Future Researchmentioning

confidence: 99%

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Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

Laakkonen¹,

Pohjolainen²

2015

SIAM J. Control Optim.

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This paper deals with frequency domain robust regulation of signals generated by an infinite-dimensional exosystem. The problem is formulated and the stability types are chosen so that one can generalize the existing finite-dimensional theory to more general classes of infinitedimensional systems and signals. The main results of this article are extensions of the internal model principle, of a necessary and sufficient solvability condition for the robust regulation problem, and of Davison's simple servo compensator for stable plants in the chosen algebraic framework. Introduction.The topic of this article is robust regulation, which is a central problem in mathematical control theory. The robust regulation problem consists of two parts: robust stabilization, and robust asymptotic tracking and disturbance rejection. Asymptotic tracking and disturbance rejection means that the error between the reference and output signals vanishes as time goes to infinity despite some disturbance signals. The reference and disturbance signals are generated by an exogenous system called the exosystem. Robustness of regulation means that the output of the closed loop asymptotically tracks the reference signals even if the plant is perturbed. Robustness is of fundamental importance since small errors in mathematical models of real-world phenomena are unavoidable and stem from various sources such as model simplifications and erroneous parameter estimation.The robust regulation problem of finite-dimensional linear multi-input multioutput (MIMO) systems was solved in the 1970s. Francis, Wonham, and Davison had a central role in this work [5,6,7,9,10]. Many authors have generalized the finitedimensional results to infinite-dimensional and nonlinear systems in the time domain as well as in the frequency domain since then [1,13,15,17,30,32,35,36,37,41].Robust regulation of signals generated by an infinite-dimensional exosystem is a challenging problem [15,39]. For the recent development on this subject, see [14,18,31] and the references therein. One can generate very general classes of signals, e.g., general periodic functions, by using infinite-dimensional exosystems. Signals that are generated by an infinite-dimensional exosystem and their frequency domain counterparts are called infinite-dimensional signals in this paper. The main emphasis in recent research has been on the time domain, while the frequency domain theory has received only a little attention. The purpose of this paper is to develop theory for robust regulation in the frequency domain.There exist multiple different rings of stable transfer functions, each of which has its own special features and is suitable for certain purposes [24]. Thus, it is natural

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Section: Concluding Discussion and Directions For Future Researchmentioning

confidence: 99%

Section: Concluding Discussion and Directions For Future Researchmentioning

confidence: 99%

Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

Laakkonen¹,

Pohjolainen²

2015

SIAM J. Control Optim.

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“…As in [6], [7], we denote with A the set of all stable, single-input-single-output, linear, finite-dimensional systems. Note that A has a commutative ring structure.…”

Section: Preliminariesmentioning

confidence: 99%

“…Firstly, such a setup encompasses within a single framework quite a general class of linear systems. For example, since we do not make any assumption on the coprime factorizability of the systems involved, our result is readily applicable also for n-D linear systems, for which computing the coprime factorization is still an open problem ( [4], [5], [6], [7]). Secondly, we can prove the validity of our result for an important class of decentralized 1-D, linear systems, namely decentralized structures that are invariant under feedback .…”

Section: Introductionmentioning

confidence: 99%

On disturbance attenuation for linear systems under stable, additive plant perturbations

Sabău

Martins

2010

Proceedings of the 2010 American Control Conference

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This paper deals with linear systems and the disturbance attenuation problem of minimizing a given operatorial norm of the lower linear fractional transformation between a generalized plant and a controller. We show that the optimal gain attainable by causal feedback does not depend on linear, stable, additive plant perturbations, irrespective of the chosen norm. The result proves applicable to an important class of decentralized control configurations. Applications to reducing the computational effort for the optimal controller synthesis are also discussed.Ş erban Sabȃu is with the Electrical and Computer Engineering Dept.,

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“…Proposition 1 of [15]) Let P be a strictly causal plant. Then any stabilizing controller of P is causal, that is, SP(P ) = S(P ).…”

Section: Preliminariesmentioning

confidence: 99%

Parametrization of delayed stabilizing controllers of multidimensional systems — Single-input single-output case

Mori

2009

2009 IEEE International Conference on Control and Automation

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Elementary Proof of Controller Parametrization Without Coprime Factorizability

Cited by 19 publications

References 24 publications

Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

On disturbance attenuation for linear systems under stable, additive plant perturbations

Parametrization of delayed stabilizing controllers of multidimensional systems — Single-input single-output case

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Elementary Proof of Controller Parametrization Without Coprime Factorizability

Cited by 19 publications

References 24 publications

Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem

On disturbance attenuation for linear systems under stable, additive plant perturbations

Parametrization of delayed stabilizing controllers of multidimensional systems &#x2014; Single-input single-output case

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Parametrization of delayed stabilizing controllers of multidimensional systems — Single-input single-output case