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Connections between diagonal stability and the secant condition for cyclic systems

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2 Author(s)
Areak, M. ; Dept. of Electr., Comput., & Syst. Eng., Rensselaer Polytech. Inst., Troy, NY ; Sontag, E.D.

We consider a class of systems with a cyclic interconnection structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a "secant condition" for stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterion to output strictly passive systems, and recover the same stability condition using our diagonal stability result as a tool for constructing a Lyapunov function. Using this procedure for Lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

Published in:

American Control Conference, 2006

Date of Conference:

14-16 June 2006

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