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Diagonal stability on cactus graphs

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1 Author(s)
Arcak, M. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA

A square matrix E is said to be diagonally stable if there exists a diagonal matrix D >; 0 satisfying DE + ET D <; 0. This notion has been instrumental in recent studies on stability of interconnected system models in communication and biological networks, in which the subsystems satisfy prescribed passivity properties and the matrix E combines this passivity information with the interconnection structure of the network. This paper presents a necessary and sufficient condition for diagonal stability when the digraph describing the structure of the matrix conforms to a “cactus” structure, which means that a pair of distinct simple circuits in the graph have at most one common vertex. In the special case of a single circuit, this diagonal stability test recovers the “secant criterion” that was recently derived for cyclic networks that commonly arise in biochemical reaction networks.

Published in:

Decision and Control (CDC), 2010 49th IEEE Conference on

Date of Conference:

15-17 Dec. 2010

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