Diagonal Stability for a Class of Interconnected Passive Systems
| dc.creator | Arcak, Murat | |
| dc.date | 2005-04-13 | |
| dc.date.accessioned | 2026-07-07T05:19:05Z | |
| dc.date.available | 2026-07-07T05:19:05Z | |
| dc.description | 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. | |
| dc.description | 10 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0504275 | |
| dc.identifier | http://arxiv.org/abs/math/0504275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74888 | |
| dc.subject | Optimization and Control | |
| dc.subject | 93D30, 93D10 | |
| dc.title | Diagonal Stability for a Class of Interconnected Passive Systems | |
| dc.type | text |