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L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming

Abstract : 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.
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https://hal.laas.fr/hal-03740522
Contributor : Dimitri Peaucelle Connect in order to contact the contributor
Submitted on : Friday, July 29, 2022 - 3:20:35 PM
Last modification on : Tuesday, October 25, 2022 - 11:58:11 AM
Long-term archiving on: : Sunday, October 30, 2022 - 6:33:29 PM

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Yoshio Ebihara, Hayato Waki, Noboru Sebe, Victor Magron, Dimitri Peaucelle, et al.. L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming. European Control Conference (ECC 2022), Jul 2022, Londres, United Kingdom. ⟨10.23919/ECC55457.2022.9838085⟩. ⟨hal-03740522⟩

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