Stability analysis with integral quadratic constraints: A dissipativity based proof

Veenman, Joost; Scherer, Carsten W.

doi:10.1109/cdc.2013.6760464

Cited by 52 publications

(65 citation statements)

References 24 publications

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“…The important point in this technical note is that the constraint P ≥ 0 on the KYP LMI solution must also be considered. Another closely related prior work is [21]. This work extends the systems with additional input/output signals to create an equivalent loop.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints

Seiler

2015

IEEE Trans. Automat. Contr.

142

178

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This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism. Index Terms-Integral quadratic constraint (IQC), linear time-invariant (LTI).

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Section: Introductionmentioning

confidence: 99%

“…A dissipation inequality based on IQCs then follows after performing a loop transformation. The work here complements [21] by focusing on the non-unique IQC factorization. This provides additional insight into the use of IQCs.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints

Seiler

2015

IEEE Trans. Automat. Contr.

142

178

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“…The relation between dissipativity (and hence Lyapunov methods) and the IQC theorem is beginning to be understood (Willems and Takaba, 2007;Veenman and Scherer, 2013;Seiler, 2015).…”

Section: The Iqc Frameworkmentioning

confidence: 99%

Zames-Falb multipliers for absolute stability: From O'Shea's contribution to convex searches

Carrasco

Turner

Heath

2015

2015 European Control Conference (ECC)

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Absolute stability attracted much attention in the sixties. Several stability conditions for loops with slope-restricted nonlinearities were developed. Results such as the Circle Criterion and the Popov Criterion form part of the core curriculum for students of control. Moreover, the equivalence of results obtained by different techniques, specifically Lyapunov and Popov's stability theories, led to one of the most important results in control engineering: the KYP Lemma.For Lurye 1 systems this work culminated in the class of multipliers proposed by O'Shea in 1966 and formalised by Zames and Falb in 1968. The superiority of this class was quickly and widely accepted. Nevertheless the result was ahead of its time as graphical techniques were preferred in the absence of readily available computer optimization. Its first systematic use as a stability criterion came twenty years after the initial proposal of the class. A further twenty years have been required to develop a proper understanding of the different techniques that can be used. In this long gestation some significant knowledge has been overlooked or forgotten. Most significantly, O'Shea's contribution and insight is no longer acknowledged; his papers are barely cited despite his original parameterization of the class.This tutorial paper aims to provide a clear and comprehensive introduction to the topic from a user's viewpoint. We review the main results: the stability theory, the properties of the multipliers (including their phase properties, phase-equivalence results and the issues associated with causality), and convex searches. For clarity of exposition we restrict our attention to continuous time multipliers for single-input single-output results. Nevertheless we include several recent significant developments by the authors and others. We illustrate all these topics using an example proposed by O'Shea himself.

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“…w (ρn) (5) where the coefficient tensor S ∈ R I1×···×In ρ ×(nx+nu)×(nx+ny) has n ρ + 2 dimensions. S is constructed from the LTI vertex systems S i1,...,in ρ .…”

Section: A Tp Model Transformationmentioning

confidence: 99%

“…The paper focuses on the polytopic LPV representation of nonlinear systems [1], [2]. The other two main LPV representations are linear fractional transformation (LFT) based LPV systems [3], [4], [5] and "grid-based" LPV systems [6], [7]. The polytopic representation of a nonlinear system can be obtained analytically [8] or numerically [9].…”

Section: Introductionmentioning

confidence: 99%

Robust Grid Point-Based Control Design for LPV Systems via Unified TP Transformation

Takarics

Yam

2015

2015 IEEE International Conference on Systems, Man, and Cybernetics

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Abstract-The paper considers a general approach for linear parameter varying (LPV) control. The approach is based on polytopic representation of the LPV system. First, a grid point based control design is applied for a set of linearized models of the LPV system. The design is based on linear time invariant (LTI) techniques. Such control design allows a larger flexibility in the controller structure than the conventional parallel distributed compensation (PDC) based polytopic control. The LPV controller is obtained by linear interpolation between the LTI controllers. The paper proposes linear matrix inequality (LMI) based convex optimization for robustness analysis of the resulting controller. The approach requires the plant and the controller to be defined by a common polytopic structure. It is proposed to obtain this common structure via unified TP model transformation. A simple numerical example shows the efficiency of the proposed control design approach.

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Stability analysis with integral quadratic constraints: A dissipativity based proof

Cited by 52 publications

References 24 publications

Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints

Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints

Zames-Falb multipliers for absolute stability: From O'Shea's contribution to convex searches

Robust Grid Point-Based Control Design for LPV Systems via Unified TP Transformation

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