An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781538654286
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2018 Annual American Control Conference, ACC 2018
Country/TerritoryUnited States

Bibliographical note

Funding Information:
The work was supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.” Peter Seiler is with the Aerospace Engineering and Mechanics Department, University of Minnesota, Email:

Publisher Copyright:
© 2018 AACC.


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