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Generalized Sarymsakov Matrices
Dalian Univ Technol, Sch Control Sci & Engn, Dalian 116024, Peoples R China..
SUNY Stony Brook, Dept Elect & Comp Engn, Stony Brook, NY 11794 USA..
Univ Groningen, Engn & Technol Inst Groningen, Fac Sci & Engn, NL-9700 Groningen, Netherlands..
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. Royal Inst Technol, Sch Elect Engn, ACCESS Linnaeus Ctr, S-11428 Stockholm, Sweden..ORCID iD: 0000-0001-9940-5929
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2019 (English)In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol. 64, no 8, p. 3085-3100Article in journal (Refereed) Published
Abstract [en]

Within the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of Sarymsakov matrices is the largest known subset that is closed under matrix multiplication, and more critically whose compact subsets are all consensus sets. This paper shows that a larger subset with these two properties can be obtained by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved by introducing the notion of the SIA index of a stochastic matrix, whose value is 1 for Sarymsakov matrices, and then exploring those stochastic matrices with larger SIA indices. In addition to constructing the larger set, this paper introduces another class of generalized Sarymsakov matrices, which contains matrices that are not SIA, and studies their products. Sufficient conditions are provided for an infinite product of matrices from this class, converging to a rank-one matrix. Finally, as an application of the results just described and to confirm their usefulness, a necessary and sufficient combinatorial condition, the "avoiding set condition," for deciding whether or not a compact set of stochastic matrices is a consensus set is revisited. In addition, a necessary and sufficient combinatorial condition is established for deciding whether or not a compact set of doubly stochastic matrices is a consensus set.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2019. Vol. 64, no 8, p. 3085-3100
Keywords [en]
Cooperative control, doubly stochastic matrices, multi-agent systems, products of stochastic matrices, Sarymsakov matrices, GROOT MH, 1974, JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, V69, P118 uri Behrouz, 2014, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, V59, P437 ndrickx Julien M., 2014, 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)53rd IEEE Annual Conference on Decision and Control (CDC), DEC 15-17, 2014, Los Angeles, CA, P2118 u Ji, 2012, 2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)51st IEEE Annual Conference on Decision and Control (CDC), DEC 10-13, 2012, HI, P3991 itsiklis J. N., 1984, Problems in decentralized decision making and computation, ndrickx Julien M., 2011, 2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC)50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC), DEC 12-15, 2011, Orlando, FL, P5070 u Ji, 2015, 2015 54TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC)54th IEEE Conference on Decision and Control (CDC), DEC 15-18, 2015, Osaka, JAPAN, P2835 vaei Javad, 2012, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, V57, P19 ao L, 2005, 2005 Fourth International Symposium on Information Processing in Sensor Networks4th International Symposium on Information Processing in Sensor Networks, APR 25-27, 2005, Los Angeles, CA, P63 uri Behrouz, 2012, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, V57, P2718
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-257569DOI: 10.1109/TAC.2018.2878476ISI: 000478694300001Scopus ID: 2-s2.0-85055720326OAI: oai:DiVA.org:kth-257569DiVA, id: diva2:1353477
Note

QC 20190923

Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2019-09-23Bibliographically approved

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Johansson, Karl H.

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