Performance optimization over positive l cones

Mohammad Naghnaeian, Petros G. Voulgaris

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


In this paper, we first consider the case where the input to a system is restricted to be in the positive cone of l, denoted by l +, and seek to characterize the system's induced norm from l+ to l. We obtain an exact characterization of this norm which is particularly easy to calculate in the case of LTI systems. Furthermore, we consider the model matching problem to show that time-varying linear or nonlinear control or filtering does not improve the performance with respect to this norm for LTI systems. In the second part of the paper, we consider the case when the output is forced to be in the positive l cone when the input is in this cone. We show if internal positivity is sought, a dynamic optimal controller offers no advantage over a static one.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781479932726
StatePublished - 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Publication series

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


Other2014 American Control Conference, ACC 2014
Country/TerritoryUnited States
CityPortland, OR


  • Linear systems
  • Observers for linear systems
  • Optimal control

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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