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EXPONENTIAL CONVERGENCE TOWARDS CONSENSUS FOR NON-SYMMETRIC LINEAR FIRST-ORDER SYSTEMS IN FINITE AND INFINITE DIMENSIONS.
- Source :
-
SIAM Journal on Mathematical Analysis . 2022, Vol. 54 Issue 3, p2727-2752. 26p. - Publication Year :
- 2022
-
Abstract
- We consider finite and infinite-dimensional first-order consensus systems with time-constant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows us to define a weighted mean corresponding to the consensus and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR systems
*LYAPUNOV functions
*FINITE, The
*DISTRIBUTED algorithms
Subjects
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 54
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 157573920
- Full Text :
- https://doi.org/10.1137/21M1416102