Fixed-Order Robust $H_{\infty}$ Controller Design With Regional Pole Assignment

Yang, Fang; Gani, Mahbub; Henrion, Didier

doi:10.1109/tac.2007.906242

Cited by 86 publications

(94 citation statements)

References 13 publications

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“…Is the described set big enough to provide any improvement at all? This question was studied in [19] and [20], besides the mentioned work [8]. The results for low orders as 2 and 3 are colorfully illustrated in [19].…”

Section: B Theoretical Justification and Detailsmentioning

confidence: 93%

Nu-Gap Model Reduction in the Frequency Domain

Sootla

2014

IEEE Trans. Automat. Contr.

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Abstract-In this paper a model reduction algorithm in the nu-gap metric is considered. The metric was originally developed to evaluate robustness of a controller for a given plant. In fact, the nu-gap metric induces the weakest topology in which stability is a robust property. All in all the nu-gap metric is perhaps the best metric to evaluate the distance between two systems in a closed loop setup. In the field of distributed control, if approximation of the subsystems is considered, such a metric can be vital for modeling purposes. The presented algorithm of model reduction in the nu-gap metric is based on semidefinite programming methods and exploits the frequency domain representation of the systems. Therefore it may be easily extended to incorporate into the optimization procedure constraints on a specific frequency region of a particular interest or the closed loop performance.

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Section: B Theoretical Justification and Detailsmentioning

confidence: 93%

Nu-Gap Model Reduction in the Frequency Domain

Sootla

2014

IEEE Trans. Automat. Contr.

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“…The big amount of articles appeared in the last decade, e.g. [8,9,10,11,12,13], demonstrates that the regional pole placement problem is still a hot topic of investigation.…”

Section: Introductionmentioning

confidence: 99%

“…The polytopic representation is one of the most used approaches for describing uncertainty or variability of the parameters in linear parameter-varying (LPV) systems. Looking at [2,5,19,7,21,8,12,13], it can be seen that a lot of effort has been put in developing techniques for regional pole placement and H 2 /H ∞ control of polytopic systems, taking advantage of some useful properties of LMIs that allow to assure that their satisfaction at some points, i.e. the vertices of the polytope, implies their satisfaction in all points inside the polytope.…”

Section: Introductionmentioning

confidence: 99%

Design of parameter-scheduled state-feedback controllers using shifting specifications

Rotondo

Nejjari

Puig

2015

Journal of the Franklin Institute

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In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H 2 control and H ∞ control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H 2 control and shifting H ∞ control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such a way that different values of these parameters imply different regions where the closed-loop poles are situated, or different performances in the H 2 or H ∞ sense. The proposed approach is derived within the so-called Lyapunov shaping paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.

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“…In [17] a positive real condition on system parameters was used to synthesise stabilizing controllers. In [18] the latter framework was extended to account for performance. The proposed method, as well, can be extended to controller design problems and numerical simulations show that it is less restrictive than [18] (see, Sec.…”

Section: Introductionmentioning

confidence: 99%

Hankel-type model reduction based on frequency response matching

Sootla

2010

49th IEEE Conference on Decision and Control (CDC)

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General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Hankel-type Model Reduction Based on Frequency Response Matching Aivar SootlaDepartment of Automatic Control, Lund University, Lund, Sweden, Box 118 SE 221 00Email: aivar@control.lth.seAbstract-In this paper, a stability preserving model reduction algorithm for single-input single-output linear time invariant systems is presented. It performs a data fitting in the frequency domain using semidefinite programming methods. Computing the frequency response of a model can be done efficiently even for large scale models making this approach applicable to those. The relaxation used to obtain a semidefinite program is similar to one used in Hankel model reduction. Therefore accuracy of approximation is also similar to Hankel model reduction one. The approach can be easily extended to frequency-weighted and parameter dependent model reduction problems.

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Fixed-Order Robust $H_{\infty}$ Controller Design With Regional Pole Assignment

Cited by 86 publications

References 13 publications

Nu-Gap Model Reduction in the Frequency Domain

Nu-Gap Model Reduction in the Frequency Domain

Design of parameter-scheduled state-feedback controllers using shifting specifications

Hankel-type model reduction based on frequency response matching

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