Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

Bachelier, Olivier; Mehdi, Driss

doi:10.1137/s036301290444349x

Cited by 14 publications

(11 citation statements)

References 29 publications

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“…The first comment is that this robust Hurwitz stability test can be easily extended to many other performances tests such as H ∞ level [1], pole clustering constraints in convex regions i. e. D-stability [8,17,32] or even pole clustering constraints in non convex regions [3,4,5]. Indeed, all those performances have been expressed in terms of inequalities such as (1) or (54).…”

Section: Discussion and Commentsmentioning

confidence: 99%

On some relaxations commonly used in the study of linear systems

Bachelier¹,

Mehdi²

2015

Kybernetika

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Section: Discussion and Commentsmentioning

confidence: 99%

On some relaxations commonly used in the study of linear systems

Bachelier¹,

Mehdi²

2015

Kybernetika

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“…Hence there is no constraint on the sign definiteness of P. This is due to the fact that the generalized KYP lemma does not invoke stability. In other words, we can have a FDI which does not induce stability and therefore P can be non-positive (see Bachelier et al 2004;Bachelier and Mehdi 2006 for more details on this issue). However, it can be easily shown that the LMI (18) in the above lemma is in fact a constraint on H ∞ norm and hence we have to impose stability because H ∞ -norm is defined (and makes sense) for stable transfer functions only.…”

Section: Stability Along the Pass Over The Finite Frequency Rangementioning

confidence: 99%

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

Paszke

Bachelier

2012

Multidim Syst Sign Process

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This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman-YakubovichPopov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.

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“…,h are 2 × 2 Hermitian matrices. This kind of description is borrowed from [3] following insights proposed in [11], [10]. Special sets can be emphasized:…”

Section: Formulation Of Smentioning

confidence: 99%

“…At this stage, it is possible to apply the generalized KalmanPopov-Yakubovich (KYP) lemma proposed in [10] (yet another application of a generalized version of the Sprocedure), with slight adaptations as in [3] (in order to encompass the caseh > 1), to claim that (15) holds if and only if there exist an Hermitian matrix P andh Hermitian positive definite matrices Q h , h = 1, . .…”

Section: Some "Augmented Lft" Solutionmentioning

confidence: 99%

“…In this paper, we make an extensive use of the notion of S-regularity inspired from that of ∂D-regularity [2], [3] and of some versions of the so-called S-procedure (see [5], [11], [19], [10] and the references therein) to derive strict LMI (sufficient) conditions for a descriptor model subject to norm-bounded LFT (Linear Fractional Transform)-based uncertainties on both matrices A and E (that are general enough to encompass many uncertainties encountered in practice). Our purpose is to propose a tool, useful at once, as simple as possible, that can be a basis for many other future works.…”

Section: Introductionmentioning

confidence: 99%

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An S-regularity approach to the robust analysis of descriptor models

Sari

Bachelier

Mehdi

2008

2008 47th IEEE Conference on Decision and Control

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This paper exploits the notion of S-regularity of a matrix pencil to propose insights for the robustness analysis of descriptor models of the form Eẋ = Ax (or Ex k+1 = Ax k for the discrete case) subject to norm-bounded LFT (Linear Fractional Transform)-based uncertainties on both matrices A and E. The property to be studied is the robust D-admissibility (robust D-stability togeteher with robust regularity and robust impulse freeness). All the proposed conditions are expressed in terms of strict LMI (Linear Matrix Inequalities). Two techniques are proposed and numerically compared.

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Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

Cited by 14 publications

References 29 publications

On some relaxations commonly used in the study of linear systems

On some relaxations commonly used in the study of linear systems

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

An S-regularity approach to the robust analysis of descriptor models

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