Inferring Global Exponential Stability Properties using Lie-bracket Approximations

arXiv (Cornell University)

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 simulated to support the theoretical findings.

Authors 2

1. Bahman Gharesifard Aachen Faculty of Electrical Engineering and Information Technology

   RWTH Aachen University

   Affiliation as printed

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

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

   RWTH Aachen University

   Affiliation as printed

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