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

Bin Hu, Márcio J. Lacerda, Peter Seiler

Research output: Contribution to journalArticlepeer-review


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
Issue number11
StatePublished - Jul 25 2017
Externally publishedYes


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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