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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 ]

Ulrich Janus

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