Abstract and Applied Analysis
Volume 2009 (2009), Article ID 198353, 13 pages
doi:10.1155/2009/198353
Research Article

A Unified Approach to High-Gain Adaptive Controllers

Ian A. Gravagne,1 John M. Davis,2 and Jeffrey J. DaCunha3

1Department of Electrical and Computer Engineering, Baylor University, Waco, TX 76798, USA
2Department of Mathematics, Baylor University, Waco, TX 76798, USA
3Spirit Global Energy Solutions, Midland, TX 79706, USA

Received 21 October 2009; Accepted 28 December 2009

Academic Editor: Allan C. Peterson

Copyright © 2009 Ian A. Gravagne et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales.