Conference proceeding
Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions
2013 American Control Conference, pp.5619-5624
06/2013
DOI: 10.1109/ACC.2013.6580717
Abstract
We present conditions that guarantee spatial uniformity in diffusively-coupled systems. Diffusive coupling is a ubiquitous form of local interaction, arising in diverse areas including multiagent coordination and pattern formation in biochemical networks. The conditions we derive make use of the Jacobian matrix and Neumann eigenvalues of elliptic operators, and generalize and unify existing theory about asymptotic convergence of trajectories of reaction-diffusion partial differential equations as well as compartmental ordinary differential equations. We present numerical tests making use of linear matrix inequalities that may be used to certify these conditions. We discuss an example pertaining to electromechanical oscillators. The paper's main contributions are unified verifiable relaxed conditions that guarantee synchrony.
Details
- Title: Subtitle
- Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions
- Creators
- S. Yusef Shafi - Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, Berkeley, CA, USAZahra Aminzare - Dept. of Math., Rutgers Univ., Piscataway, NJ, USAMurat Arcak - Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, Berkeley, CA, USAEduardo D Sontag - Dept. of Math., Rutgers Univ., Piscataway, NJ, USA
- Resource Type
- Conference proceeding
- Publication Details
- 2013 American Control Conference, pp.5619-5624
- Publisher
- IEEE
- DOI
- 10.1109/ACC.2013.6580717
- ISSN
- 0743-1619
- eISSN
- 2378-5861
- Language
- English
- Date published
- 06/2013
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9984065879602771
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