TY - GEN
T1 - L2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming
AU - Ebihara, Yoshio
AU - Motooka, Hayato
AU - Waki, Hayato
AU - Sebe, Noboru
AU - Magron, Victor
AU - Peaucelle, Dimitri
AU - Tarbouriech, Sophie
N1 - Funding Information:
Y. Ebihara and H. Motooka are with the Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan. H. Waki is with the Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan. N. Sebe is with the Department of Intelligent and Control Systems, Kyushu Institute of Technology, Fukuoka 820-8502, Japan. V. Magron, D. Peaucelle, and S. Tarbouriech are with LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France. This work was supported by JSPS KAKENHI Grant Number JP20H04145 and JP21H01354.
Publisher Copyright:
© 2022 EUCA.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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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U2 - 10.23919/ECC55457.2022.9838085
DO - 10.23919/ECC55457.2022.9838085
M3 - Conference contribution
AN - SCOPUS:85136707508
T3 - 2022 European Control Conference, ECC 2022
SP - 1385
EP - 1390
BT - 2022 European Control Conference, ECC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 European Control Conference, ECC 2022
Y2 - 12 July 2022 through 15 July 2022
ER -