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IMA Journal of Mathematical Control and Information Advance Access originally published online on August 25, 2009
IMA Journal of Mathematical Control and Information 2009 26(3):319-323; doi:10.1093/imamci/dnp015
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A counter example to a recent result on the stability of non-linear systems

Shah Muhammad{dagger} and Jacob van der Woude

Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands

{dagger} Email: s.muhammad{at}tudelft.nl

Received on April 14, 2009; Revision received April 14, 2009. Accepted on May 11, 2009

Langson & Alleyne (2002, J Dyn. Syst. Meas. Control, 124, 452–456) proposed certain sufficient conditions that guarantee the global asymptotic stability of a class of non-linear systems. In this paper, we give a counter example to demonstrate that the conditions stated in Langson & Alleyne (2002) are not sufficient for the global asymptotic stability.

Keywords: non-linear systems; state-dependent coefficient parametrization; global asymptotic stability.


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