On ℓ performance optimization of switched systems

Shengxiang Jiang, Petros G. Voulgaris

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


In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n given linear time invariant (LTI) systems. The interest is placed on minimizing the worst case ℓ -induced norm of this model matching system over all possible switchings. This minimization is performed over all Youla-Kucera parameters Q that switch causally in time over n (stable) LTI systems. For the particular set-up at hand, it is shown that the optimal Youla-Kucera parameter Q need not depend on the switching sequence in the case of partially matched switching, and that it can be obtained as an LTI solution to an associated standard ℓ1 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in linear programming, and an approximate solution with any given precision is possible by finite truncation.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424414989, 9781424414987
StatePublished - 2007
Externally publishedYes
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other46th IEEE Conference on Decision and Control 2007, CDC
Country/TerritoryUnited States
CityNew Orleans, LA


  • Worst case switching

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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