Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 55, Issue 6, Pages 1484-1487Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2045694
Keywords
Diagonal stability; positive linear systems; stability of linear systems
Funding
- National Science Foundation (NSF) [ECCS-0824118]
- Science Foundation of Ireland (SFI) [07/IN/I1901]
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In this note, a simple method is presented that is both necessary and sufficient for determining whether a given Metzler matrix A is Hurwitz. The method is based on the well known fact that a Hurwitz Metzler matrix is also diagonally stable. By using this fact, very simple conditions are derived for the Hurwitz stability of a Metzler matrix. The conditions are stated in terms of the signs of the diagonal entries of a sequence of lower dimensional matrices. The efficacy of the conditions is demonstrated by applying them to determine stability in several examples.
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