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Diagonal Stability for a Class of Interconnected Passive Systems

Authors
  • Arcak, Murat
Type
Preprint
Publication Date
Apr 13, 2005
Submission Date
Apr 13, 2005
Identifiers
arXiv ID: math/0504275
Source
arXiv
License
Unknown
External links

Abstract

We consider a class of matrices with a specific structure that arises, among other examples, in dynamic models for biological regulation of enzyme synthesis (Tyson and Othmer, 1978). We first show that a stability condition given in (Tyson and Othmer, 1978) is in fact a necessary and sufficient condition for diagonal stability of this class of matrices. We then revisit a recent generalization of (Tyson and Othmer, 1978) to nonlinear systems given in (Sontag, 2005), and recover the same stability condition using our diagonal stability result. Unlike the input-output based arguments employed in (Sontag, 2005), our proof gives a procedure to construct a Lyapunov function. Finally we study static nonlinearities that appear in the feedback path, and give a stability condition that mimics the Popov criterion.

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