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IMA Journal of Mathematical Control and Information 2003 20(1):129-136; doi:10.1093/imamci/20.1.129
© 2003 by Institute of Mathematics and its Applications
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On the generalized Aizerman–Myshkis problem for retarded distributed parameters systems

M. I. Gil'1

1 Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel

We consider a class of nonlinear distributed parameters retarded systems governed by differential-delay equations in a Hilbert space. The considered equations have separated linear parts and sublinear nonlinearities. Explicit conditions are established for the absolute stability. Moreover, it is shown that these conditions separate equations that satisfy the generalized Aizerman–Myshkis hypothesis.

Keywords: nonlinear distributed parameters retarded systems; absolute stability; the Aizerman–Myshkis problem.

Received 14 February 2002. Accepted 1 May 2002.


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