Bounds for uncertain matrix root‐clustering in a union of subregions

Bachelier, O.; Pradin, B.

doi:10.1002/(sici)1099-1239(199905)9:6<333::aid-rnc408>3.3.co;2-z

Cited by 3 publications

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“…In Peaucelle et al (2000), D R -regions were shown to be able to describe non-convex regions but only represented symmetrically, which motivated Bosche, Bachelier, and Mehdi (2005) to extend the concept further to consider non-symmetrical regions. On the other hand, Bachelier and Pradin (1999) developed an approach that allows specifying not only a simple convex region, but also a non-convex region, defined as a union of convex subregions. Then, Maamri, Bachelier, and Mehdi (2006) proposed a technique in order to achieve partial pole placement via aggregation in such regions.…”

Section: Introductionmentioning

confidence: 99%

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LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions

Yang

Rotondo

Puig

2021

International Journal of Systems Science

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This paper introduces an approach for the design of a state-feedback controller for LPV systems that achieves pole clustering in a union of DR-regions. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities, which can be solved efficiently using available solvers. In addition, it is shown that the approach can be modified in a shifting sense, which means that the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated, thus enabling online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations. KEYWORDSLinear parameter varying (LPV) systems, pole placement, union of regions, linear matrix inequalities (LMIs), state-feedback control.

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Section: Introductionmentioning

confidence: 99%

“…Without any assumption on the matrix R 11 , D R -regions are not convex, but with R 11 0, D R -regions become a slight modification of the characterization provided by LMI regions (Rotondo, 2017). In Bachelier and Pradin (1999), non-convex regions were considered as unions of convex subregions.…”

Section: Introductionmentioning

confidence: 99%

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions

Yang

Rotondo

Puig

2021

International Journal of Systems Science

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Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

Chen

Chou

Zheng

2006

Journal of Dynamic Systems, Measurement, and Control

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In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

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Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

Bachelier¹,

Mehdi²

2006

SIAM J. Control Optim.

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Bounds for uncertain matrix root‐clustering in a union of subregions

Cited by 3 publications

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LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

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Bounds for uncertain matrix root‐clustering in a union of subregions

Cited by 3 publications

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LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟R-regions

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟R-regions

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

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LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟_R-regions