Differential-algebraic inclusions with maximal monotone operators

Kanat Camlibel, Luigi Iannelli, Aneel Tanwani*, Stephan Trenn

*Corresponding author for this work

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

4 Citations (Scopus)


The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion equation for a symmetric positive semi-definite matrix P ϵ ℝn×n, and a maximal monotone operator M : ℝn → ℝn. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only Px is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation.

Original languageEnglish
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781509018376
Publication statusPublished - 27-Dec-2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: 12-Dec-201614-Dec-2016


Conference55th IEEE Conference on Decision and Control, CDC 2016
Country/TerritoryUnited States
CityLas Vegas

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