A general framework for robust analysis and control: an integral quadratic constraint based approach

Joost Veenman

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Joost Veenman, A general framework for robust analysis and control: an integral quadratic constraint based approach (2015), Logos Verlag, Berlin, ISBN: 9783832595012

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Beschreibung / Abstract

In this thesis we are concerned with the robustness analysis and control of uncertain systems. We built upon a powerful framework, the so-called integral quadratic constraint (IQC) approach, which enables us, not only to efficiently perform robust stability and performance analysis for a large class of uncertain systems, but also to systematically design robust controllers via solving linear matrix inequalities (LMIs) and convex optimization problems. Indeed, as main contribution, we reveal that the IQC-framework is not only useful for analysis purposes, but also has great potential for a rather diverse class of synthesis questions, some of which have already been addressed in the literature, while others have not. This includes scenarios such as nominal output feedback control, nominal gain-scheduling control, robust estimator or observer design, robust feedforward control, generalized l2-synthesis, multi-objective and structured controller synthesis, robust open-loop controller synthesis, gain-scheduling control with uncertain performance weights and robust controller synthesis with unstable weight, among others.

Inhaltsverzeichnis

  • BEGINN
  • 1 Introduction
  • 1.1 Motivation
  • 1.2 Aim and main goals of the thesis
  • 1.3 Outline and contributions
  • 2 Stability analysis with integral quadratic constraints
  • 2.1 Introduction
  • 2.2 A specific feedback interconnection
  • 2.3 Stability analysis with integral quadratic constraints
  • 2.4 Robust stability and performance analysis
  • 2.5 From infinite to finite dimensional feasibility tests
  • 2.6 IQC-multipliers for uncertainties and nonlinearities
  • 2.7 IQC-multipliers for performance
  • 2.8 Further connections and possibilities
  • 2.9 Illustrations
  • 2.10 An alternative proof of the IQC-theorem
  • 2.11 Chapter summary
  • 3 From analysis to synthesis
  • 3.1 Introduction
  • 3.2 Robust controller synthesis
  • 3.3 Gain-scheduled controller synthesis
  • 3.4 Robust gain-scheduled controller synthesis
  • 3.5 Preparations
  • 3.6 Nominal controller synthesis
  • 3.7 Nominal gain-scheduled controller synthesis
  • 3.8 Outline of further possible configurations
  • 3.9 Chapter summary
  • 4 Robust gain-scheduled estimation
  • 4.1 Introduction
  • 4.2 The robust gain-scheduled estimation problem
  • 4.3 Robust stability and performance analysis
  • 4.4 From analysis to synthesis
  • 4.5 A convex solution
  • 4.6 Illustrations
  • 4.7 Chapter summary
  • 5 Another general synthesis framework
  • 5.1 Introduction
  • 5.2 A generic feasibility problem
  • 5.3 A convex solution
  • 5.4 Robust gain-scheduling control for systems without control-channel uncertainties
  • 5.5 Concrete applications
  • 5.6 Illustrations
  • 5.7 Summary
  • 6 IQC-synthesis with warm-start options
  • 6.1 Introduction
  • 6.2 Problem formulation
  • 6.3 Nominal controller synthesis and robust analysis
  • 6.4 From analysis to synthesis
  • 6.5 On the factorization of IQC-multipliers
  • 6.6 Warm-start techniques for robust controller synthesis
  • 6.7 IQC-synthesis with warm-start options
  • 6.8 Illustrations
  • 6.9 Summary
  • 7 Conclusions and recommendations
  • 7.1 Conclusions
  • 7.2 Recommendations for future research
  • Appendices
  • A Explanation of symbols
  • B Abbreviations
  • C Dualization and elimination
  • D A particular version of the KYP-Lemma
  • E Introducing and removing dynamics in LMIs
  • F Operations on FDIs and their corresponding LMIs
  • G On the factorization of rational matrix functions

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