Maximal perturbation bounds for robust α-stability of matrix second-order systems with one-parameter perturbations

In this paper, the robust α-stability problem of matrix second-order systems with perturbations in the form of a one-parameter family of matrices is investigated. All the system matrices, including the second-order differential coefficient matrices, are assumed to have such perturbations. Based on t...

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Bibliographic Details
Published in:Automatica (Oxford) 2012-05, Vol.48 (5), p.995-998
Main Authors: Lu, Jun-Guo, Xiao, Jizhong, Chen, Weidong
Format: Article
Language:English
Subjects:
Applied sciences
Coefficient perturbation
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Exact sciences and technology
Perturbation bound
Robust stability
Second-order system
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Summary:In this paper, the robust α-stability problem of matrix second-order systems with perturbations in the form of a one-parameter family of matrices is investigated. All the system matrices, including the second-order differential coefficient matrices, are assumed to have such perturbations. Based on the Kronecker product, a necessary and sufficient condition for the robust α-stability problem is presented by transforming such a problem into checking the nonsingularity of a class of uncertain matrices. Then, a closed form for the maximal perturbation bounds for preserving the α-stability is given. Finally, illustrative examples are given to show that our results are effective and less conservative than the results obtained by other researchers.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2012.02.042