@inproceedings{e8ebeec8d6f2408bb2dd4511cb769e9b,
title = "Stability analysis of positive bilinear control systems: A variational approach",
abstract = "We consider a continuous-time bilinear control system with Metzler matrices. The transition matrix of such a system is entrywise nonnegative, and the positive orthant is an invariant set of the dynamics. Motivated by the stability analysis of positive linear switched systems (PLSSs), we define a control as optimal if, for a fixed final time, it maximizes the spectral radius of the transition matrix. A recent paper [1] developed a first-order necessary condition for optimality in the form of a maximum principle (MP). In this paper, we derive a stronger, second-order necessary condition for optimality for both singular and bang-bang controls. Our approach is based on combining results on the second-order derivative of the spectral radius of a nonnegative matrix with the generalized Legendre-Clebsch condition and the Agrachev-Gamkrelidze second-order variation.",
author = "Gal Hochma and Michael Margaliot",
year = "2013",
doi = "https://doi.org/10.1109/CDC.2013.6760071",
language = "الإنجليزيّة",
isbn = "9781467357173",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1355--1359",
booktitle = "2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013",
address = "الولايات المتّحدة",
note = "52nd IEEE Conference on Decision and Control, CDC 2013 ; Conference date: 10-12-2013 Through 13-12-2013",
}