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Published in:
2008 | OriginalPaper | Chapter
Stability of Dynamical Systems via Semidefinite Programming
Authors : Mihály Bakonyi, Kazumi N. Stovall
Published in: Recent Advances in Matrix and Operator Theory
Publisher: Birkhäuser Basel
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In this paper, we study stability of nonlinear dynamical systems by searching for Lyapunov functions of the form
$$ \Lambda (x) = \sum\limits_{i = 1}^m {\alpha _i x_i } + \frac{1} {2}\sum\limits_{i = 1}^m {\lambda _i x_1^2 } ,\lambda _i > 0,i = 1, \ldots ,m $$
, 0,
i
= 1,...,
m
, respectively
x
T
Ax
, where A is a positive definite real matrix. Our search for Lyapunov functions is based on interior point algorithms for solving certain positive definite programming problems and is applicable for non-polynomial systems not considered by similar methods earlier.