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IMA Journal of Mathematical Control and Information 2002 19(1 and 2):59-72; doi:10.1093/imamci/19.1_and_2.59
© 2002 by Institute of Mathematics and its Applications
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Nonlinear delay systems, Lie algebras and Lyapunov transformations

S. P. Banks1

1 Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

In this paper we consider nonlinear delay systems of the form (t) = A(x(t), x(t – {delta}))x(t) + B(x(t), x(t – {delta}))u(t) and obtain new stability and control results by replacing the system by a sequence of linear, time-varying systems and using an explicit representation for the solution of such systems in terms of a Lie algebra associated with the system. In the case of nilpotent Lie algebras we use a Lyapunov transformation to prove stability.

Keywords: Lie algebras; nonlinear delay systems; Lyapunov transformation.


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