Diagonal Stability for a Class of Interconnected Passive Systems

Details Diagonal Stability for a Class of Interconnected Passive Systems Diagonal Stability for a Class of Interconnected Passive Systems

2005-04-13

arxiv.org/abs/math/0504275v1

Mathematics

Optimization and Control

10 pages, 4 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Diagonal Stability for a Class of Interconnected Passive Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Diagonal Stability for a Class of Interconnected Passive Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diagonal Stability for a Class of Interconnected Passive Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-249926