Robust synthesis for linear parameter varying systems using integral quadratic constraints

Shu Wang, Harald Pfifer, Peter Seiler

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations


A robust synthesis algorithm is proposed for a class of uncertain linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal (not-uncertain) LPV system and an uncertainty whose input/output behavior is described by an integral quadratic constraint (IQC). The proposed algorithm is a coordinate-wise ascent that is similar to the well-known DK iteration for μ-synthesis. In the first step, a nominal controller is designed for the LPV system without uncertainties. In the second step, the robustness of the designed controller is evaluated and a new scaled plant for the next synthesis step is created. The robust performance condition used in the analysis step is formulated as a dissipation inequality that incorporates the IQC and generalizes the Bounded Real Lemma like condition for performance of nominal LPV systems. Both steps can be formulated as a semidefinite program (SDP) and efficiently solved using available optimization software. The effectiveness of the proposed method is demonstrated on a simple numerical example.

Original languageEnglish (US)
Article number7040136
Pages (from-to)4789-4794
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Grant #NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms” and IREE Project RL-0011-13 “Innovating for Sustainable Electricity Systems: Integrating Variable Renewable, Regional Grids, and Distributed Resources”. The material in this paper was partially presented at the 53rd IEEE Conference on Decision and Control, December 15–17, 2014, Los Angeles, CA, USA. This paper was recommended for publication in revised form by Associate Editor Fen Wu under the direction of Editor Richard Middleton.

Publisher Copyright:
© 2014 IEEE.

Copyright 2016 Elsevier B.V., All rights reserved.


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