Journal Article

Nonlinear delay systems, Lie algebras and Lyapunov transformations

S. P. Banks

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 19, issue 1_and_2, pages 59-72
Published in print March 2002 | ISSN: 0265-0754
Published online March 2002 | e-ISSN: 1471-6887 | DOI:
Nonlinear delay systems, Lie algebras and Lyapunov transformations

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In this paper we consider nonlinear delay systems of the form (t) = A(x(t), x(t – δ))x(t) + B(x(t), x(t – δ))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

Journal Article.  0 words. 

Subjects: Mathematics

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