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Vietnam
Journal of Mathematics 37:2&3 (2009) 339-356
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Maximal Stability Bound for Generalized Singularly
Perturbed Systems
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Vu Hoang Linh and Nguyen
Quoc Tuan
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Abstract. In this paper, we propose
computable formulas for the maximal stability bound for implicit systems of
linear differential equations which contain an uncertain small parameter in
the leading term. It is supposed that the systems are previously transformed
into an appropriate sparse form and they are robustly stable. To find the
maximal stability bound of the systems, the time-domain method is used.
This leads to generalized eigenvalue problems for matrix pencils. Details
of the numerical algorithms and some illustrative examples are given.
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2000 Mathematics Subject Classification: 34A09, 34D15,
93D09.
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Keywords: Stability bound, asymptotic stability,
implicit system, index of matrix pencils, singularly perturbed system,
generalized eigenvalue problem, Kronecker sum and product.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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