Inferring Global Exponential Stability Properties using Lie-bracket Approximations

Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes, pp. 6274–6279

Abstract

In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to their associated Lie-bracket systems is shown. The result is applied to adapt dither frequencies to find a sufficiently high gain in adaptive control of linear unknown systems, and a simple numerical example is provided to support the theoretical findings.

Authors 2

1. Bahman Gharesifard

   University of California, Los Angeles

   Affiliation as printed

   University of California,Electrical & Computer Engineering Department,Los Angeles,USA

2. Christian Ebenbauer Aachen Faculty of Electrical Engineering and Information Technology

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Faculty of Electrical Engineering and Information Technology,Aachen,Germany,D-52074