January 30, 2006

D stability references

Had a chat with Iulian and got some references off him on D-stability

• The $D$-stability problem for $4\times 4$ real matrices
Serkan T. Impram, Russell Johnson, Raffaella Pavani [ PDF ].
• A Simple and Less Conservative Test for ${\Bbb D}$-Stability
Ricardo C. L. F. Oliveira, Pedro L. D. Peres [ DOI ]
• D-Stability from a Numerical Point of View,
Raffaella Pavani, Politecnico di Milano, Italy [ PDF ]
• this document states theorem on D-stability linking it with mixing stability like conditions:
http://cepa.newschool.edu/het/essays/get/local.htm#dynamic

Other notes matrix stabiliy:

• Hurwitz criterion too expensive for high dimentions
• Sign stability: most matrices of biochemical systems are not sign stable, so not a useful criterion
• most promising: find good criteria for D-stabiliy. rumour has it that the commercial LMA toolbox for matlab, which deals with matrix inequalities, might be able to help. orr maybe SciLab as the non-commercial substitute.

And finally we have also books about that, e.g.

• Matrix Diagonal Stability in Systems and Computation (Hardcover)
by Eugenius Kaszkurewicz, Amit Bhaya [ at Amazon ] [ and here ]

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