Robustness analysis of uncertain discrete-time systems with dissipation inequalities and integral quadratic constraints

Bin Hu, Márcio J. Lacerda, Peter Seiler

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9 Scopus citations

Abstract

This paper presents a connection between dissipation inequalities and integral quadratic constraints (IQCs) for robustness analysis of uncertain discrete-time systems. Traditional IQC results derived from homotopy methods emphasize an operator-theoretic input–output viewpoint. In contrast, the dissipativity-based IQC approach explicitly incorporates the internal states of the uncertain system, thus providing a more direct procedure to analyze uniform stability with non-zero initial states. The standard dissipation inequality requires a non-negative definite storage function and ‘hard’ IQCs. The term ‘hard’ means that the IQCs must hold over all finite time horizons. This paper presents a modified dissipation inequality that requires neither non-negative definite storage functions nor hard IQCs. This approach leads to linear matrix inequality conditions that can provide less conservative results in terms of robustness analysis. The proof relies on a key J-spectral factorization lemma for IQC multipliers. A simple numerical example is provided to demonstrate the utility of the modified dissipation inequality.

Original languageEnglish (US)
Pages (from-to)1940-1962
Number of pages23
JournalInternational Journal of Robust and Nonlinear Control
Volume27
Issue number11
DOIs
StatePublished - Jul 25 2017

Bibliographical note

Funding Information:
The authors acknowledge helpful comments and discussions with Joaquin Carrasco, Andrew Packard, Sei Zhen Khong, Mazen Farhood, and Anders Rantzer. The work was supported by the National Science Foundation Grant No. NSF-CMMI-1254129 entitled ?CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms? and the NASA Langley NRA Cooperative AgreementNNX12AM55A entitled ?Analytical Validation Tools for Safety Critical Systems Under Loss-of Control Conditions?, Dr. Christine Belcastro technical monitor. It was also supported by the S?o Paulo Research Foundation (FAPESP) grant 2015/00269-5.

Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.

Keywords

  • J-spectral factorizations
  • dissipation inequalities
  • integral quadratic constraints
  • robustness analysis
  • uncertain discrete-time systems

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