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IMA Journal of Mathematical Control and Information Advance Access originally published online on July 27, 2005
IMA Journal of Mathematical Control and Information 2006 23(1):67-84; doi:10.1093/imamci/dni044
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

On the robust stability of implicit linear systems containing a small parameter in the leading term

Nguyen Huu Du and Vu Hoang Linh**

Faculty of Mathematics, Mechanics, and Informatics, University of Natural Sciences, Vietnam National University, 334, Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam

** Email: vhlinh{at}hn.vnn.vn

This paper deals with the robust stability of implicit linear systems containing a small parameter in the leading term. Based on possible changes in the algebraic structure of the matrix pencils, a classification of such systems is given. The main attention is paid to the cases when the appearance of the small parameter causes some structure change in the matrix pencil. First, we give sufficient conditions providing the asymptotic stability of the parameterized system. Then, we give a formula for the complex stability radius and characterize its asymptotic behaviour as the parameter tends to zero. The structure-invariant cases are discussed, too. A conclusion concerning the parameter dependence of the robust stability is obtained.

Keywords: robust stability; stability radius; singular perturbation; implicit systems; dependence on parameter.

Received on 27 July 2004. revised on 9 January 2005. accepted on 12 January 2005.


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