L2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming

Yoshio Ebihara, Hayato Motooka, Hayato Waki, Noboru Sebe, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech

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


This paper is concerned with the analysis of the L2 induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L2+ induced norm in this paper. It has been shown very recently that the L2+ induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L2+ induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming.

Original languageEnglish
Title of host publication2022 European Control Conference, ECC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783907144077
Publication statusPublished - 2022
Event2022 European Control Conference, ECC 2022 - London, United Kingdom
Duration: Jul 12 2022Jul 15 2022

Publication series

Name2022 European Control Conference, ECC 2022


Conference2022 European Control Conference, ECC 2022
Country/TerritoryUnited Kingdom

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Networks and Communications
  • Information Systems and Management
  • Control and Systems Engineering
  • Control and Optimization
  • Modelling and Simulation


Dive into the research topics of 'L2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming'. Together they form a unique fingerprint.

Cite this