Finite horizon robustness analysis of LTV systems using integral quadratic constraints

Peter Seiler, Robert M. Moore, Chris Meissen, Murat Arcak, Andrew Packard

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as an interconnection of a known LTV system and a perturbation. The input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Typical notions of robustness, e.g. nominal stability and gain/phase margins, can be insufficient for finite-horizon analysis. Instead, this paper focuses on robust induced gains and bounds on the reachable set of states. Sufficient conditions to compute robust performance bounds are formulated using dissipation inequalities and IQCs. The analysis conditions are provided in two equivalent forms as Riccati differential equations and differential linear matrix inequalities, and an algorithm is developed leveraging both forms.

Original languageEnglish (US)
Pages (from-to)135-143
Number of pages9
StatePublished - Feb 2019

Bibliographical note

Funding Information:
The material in this paper was not presented at any conference. The authors acknowledge funding from ONR, United States project N00014-18-1-2209. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton.

Publisher Copyright:
© 2018 Elsevier Ltd


  • Integral quadratic constraints
  • Linear time varying
  • Robustness


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