Stability analysis of positive bilinear control systems: A variational approach

Gal Hochma, Michael Margaliot

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1355-1359
Number of pages5
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 10 Dec 201313 Dec 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference52nd IEEE Conference on Decision and Control, CDC 2013
Country/TerritoryItaly
CityFlorence
Period10/12/1313/12/13

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