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Vietnam Journal of Mathematics 37:2&3 (2009) 339-356 

Maximal Stability Bound for Generalized Singularly Perturbed Systems

Vu Hoang Linh and Nguyen Quoc Tuan

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.

2000 Mathematics Subject Classification: 34A09, 34D15, 93D09.

Keywords: Stability bound, asymptotic stability, implicit system, index of matrix pencils, singularly perturbed system, generalized eigenvalue problem, Kronecker sum and product.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society
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