An LMI-based stability analysis for adaptive controllers

Authors:
Bong-Jun Yang;Tansel Yucelen;Anthony J. Calise;Jong-Yeob Shin
Affiliations:
Guided Systems Technologies, Inc., McDonough, GA;School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA;School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA;Gulfstream Aerospace Corporation, Savannah, GA
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 3
Cited 0

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Abstract

We develop a Linear Matrix Inequality (LMI) tool for analyzing the stability and performance of adaptive controllers that employ σ-modification. The formulation involves recasting the error dynamics composed of the tracking error and the weight estimator error into a linear parameter varying form. We show how stability, convergence rate, domain of attraction, and the transient and steady state behavior of the adaptive control system can be analyzed using the developed LMI tool. It is guaranteed that less conservative estimates for the convergence rate and the size of the ultimate bound for the tracking error are obtained compared to the standard analysis in the literature.