An LMI-based stability analysis for adaptive controllers

We develop a Linear Matrix Inequality (LMI) tool for analyzing the stability and performance of adaptive controllers that employ sigma-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.