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A New Sufficient Condition for Additive D-Stability and Application to Cyclic Reaction-Diffusion Models

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2 Author(s)
Xiaoqing Ge ; Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA ; Murat Arcak

Matrix A is said to be additively D-stable if A-D remains Hurwitz for all nonnegative diagonal matrices D. In reaction-diffusion models, additive D-stability of the matrix describing the reaction dynamics guarantees stability of the homogeneous steady-state, thus ruling out the possibility of diffusion-driven instabilities. We present a new criterion for additive D-stability using the concept of compound matrices. We first give conditions under which the second additive compound matrix has nonnegative off-diagonal entries. We then use this Metzler property of the compound matrix to prove additive D-stability with the help of an additional determinant condition. This result is then applied to investigate stability of cyclic reaction networks in the presence of diffusion.

Published in:

2009 American Control Conference

Date of Conference:

10-12 June 2009