Paper Info
Title
A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure
Abstract
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns. In this paper, a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified. For these systems global stability results hold if the "secant" criterion is satisfied. In the linear case, it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic Lyapunov function, which extends a recent diagonal stability result to partial differential equations. For reaction-diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established. All of the derived results remain true for both linear and nonlinear positive diffusion terms. Similar results are shown for compartmental systems.
Year
DOI
Venue
2008
10.1109/TAC.2007.911318
IEEE Transactions on Circuits and Systems I-regular Papers
Keywords
Field
DocType
Negative feedback,Jacobian matrices,Stability criteria,Asymptotic stability,Neurofeedback,Oscillators,Lyapunov method,Partial differential equations,Nonlinear equations,Couplings
Passivity,Ethylene,Polymer,Copolymer,Spinning,Computer science,Mathematical analysis,Control theory,Chemical engineering,Interconnection
Journal
Volume
Issue
ISSN
53
Special Issue
0018-9286
Citations 
PageRank 
References 
22
2.53
5
Authors
3
Name
Order
Citations
PageRank
Mihailo R. Jovanovic159455.52
murat arcak21855195.31
Eduardo D. Sontag33134781.88