Robust stability and performance analysis based on integral quadratic constraints

Veenman, Joost; Scherer, Carsten W.; Köroğlu, Hakan

doi:10.1016/j.ejcon.2016.04.004

Cited by 141 publications

(190 citation statements)

References 117 publications

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“…This set of diagonally repeated circle criterion multipliers is given by

\begin{matrix} right {normalΠ}_{d r} {[α, β]}^{k} = \{normalΠ \in S^{2 k} | normalΠ = (\begin{matrix} - α β diag (λ_{j}) & \frac{α + β}{2} diag (λ_{j}) \\ \frac{α + β}{2} diag (λ_{j}) & - diag (λ_{j}) \end{matrix}), λ \in R^{k}, λ_{j} > 0\} . \end{matrix}

As will be seen, unstructured multipliers offer more freedom. Let us hence introduce the class of full‐block circle criterion multipliers (, Section 5.8.2.) adapted to the diagonally repeated case.…”

Section: Derivation and Application Of Full‐block Multipliersmentioning

confidence: 99%

“…Obviously, more freedom in the choice of H , that is, increasing the dimension of the considered subspaces, leads in general to improved results but also causes higher computational complexity. In the sequel, we present an approach that allows to balance both by extending the ideas for the scalar case , which rely on a family of dense subspaces of

ℒ_{1}

. Fix a real pole ρ <0.…”

Section: Derivation and Application Of Full‐block Multipliersmentioning

confidence: 99%

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Full‐block multipliers for repeated, slope‐restricted scalar nonlinearities

Fetzer

Scherer

2017

Intl J Robust & Nonlinear

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Summary This paper provides a comprehensive treatment of full‐block multipliers within the integral quadratic constraints framework for stability analysis of feedback systems containing repeated, slope‐restricted scalar nonlinearities. We develop a novel stability result that offers more flexibility in its application because it allows for the inclusion of general Popov and Yakubovich criteria in combination with the well‐established Circle and Zames‐Falb stability tests within integral quadratic constraint theory. A particular focus lies on the formulation of stability criteria in terms of full‐block multipliers, some of which are new, and thus typically involve less conservatism than current methods. Furthermore, a new asymptotically exact parametrization of full‐block Zames‐Falb multipliers is given that allows to exploit the complete potential of this stability test. Copyright © 2017 John Wiley & Sons, Ltd.

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“…This set of diagonally repeated circle criterion multipliers is given by

\begin{matrix} right {normalΠ}_{d r} {[α, β]}^{k} = \{normalΠ \in S^{2 k} | normalΠ = (\begin{matrix} - α β diag (λ_{j}) & \frac{α + β}{2} diag (λ_{j}) \\ \frac{α + β}{2} diag (λ_{j}) & - diag (λ_{j}) \end{matrix}), λ \in R^{k}, λ_{j} > 0\} . \end{matrix}

Section: Derivation and Application Of Full‐block Multipliersmentioning

confidence: 99%

ℒ_{1}

. Fix a real pole ρ <0.…”

Section: Derivation and Application Of Full‐block Multipliersmentioning

confidence: 99%

Full‐block multipliers for repeated, slope‐restricted scalar nonlinearities

Fetzer

Scherer

2017

Intl J Robust & Nonlinear

Self Cite

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show abstract

“…In fact, only the largest airspeed at which the system settles down to the original equilibrium when subject to any vanishing perturbation can be inferred. It is well understood in the literature [1], [7], [9] that results holding locally can greatly improve the analysis of systems via IQC. Therefore now the IQC description of the nonlinearity is relaxed by considering a local sector constraint definition.…”

Section: B Local Analysismentioning

confidence: 99%

“…Then, in the IQC approach, conservatism of the analyses in terms of selection of the multipliers and global validity of the results are investigated and possible strategies to address them are proposed. These two issues represent an active area of research in IQC analysis [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability and post-critical analysis of an uncertain plant with describing functions and integral quadratic constraints

Iannelli

Marcos

Lowenberg

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…For minimal state space representations of these transfer functions we refer reader to [32], [42], [43].…”

Section: A Parametrizationsmentioning

confidence: 99%

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

Tugal

Carrasco

Falcon

et al. 2017

IEEE Trans. Contr. Syst. Technol.

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Abstract-This paper provides less conservative stability conditions for bilateral teleoperation by exploiting the advantages of the integral quadratic constraint (IQC) framework, where the environment can be defined as a memoryless, bounded, and monotonic nonlinear operator. Recent advances in multiplier theory for appropriate classes of uncertainties/nonlinearities are applied. Since the classes of multipliers have infinite dimension, parametrization of these multipliers is used to obtain convex searches over a finite number of parameters. The stability of the system is analysed as a Lurye system containing timedelay and monotone nonlinearity. As a result, less conservative delay-dependent conditions can be developed. These results are then applied to bilateral teleoperation. Finally, stability results are tested with different experiments; in particular bilateral teleoperation experiments over the internet between Manchester, UK, and Vigo, Spain, have been carried out. The advantage of the proposed approach is demonstrated by reaching higher transparency index for 2-channel position-force teleoperation while ensuring absolute stability.

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Robust stability and performance analysis based on integral quadratic constraints

Cited by 141 publications

References 117 publications

Full‐block multipliers for repeated, slope‐restricted scalar nonlinearities

Full‐block multipliers for repeated, slope‐restricted scalar nonlinearities

Nonlinear stability and post-critical analysis of an uncertain plant with describing functions and integral quadratic constraints

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

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