Parameter Convergence of Modified Adaptive Laws with Persistent Excitation

An important property of adaptive laws without robustness modifications and in the absence of plant uncertainties is the exponential convergence of the estimated parameters to their true ones under some persistent excitation (PE) condition on the information signal vector. When the adaptive laws are modified for robustness this ideal property of parameter convergence may no longer be maintained due to the effect of the modifications on the convergence properties of the adaptive law. In this paper we examine the effect of the switching-¿ modification on the exponential convergence of parameter estimates for two different adaptive laws. We show that the switching-¿ modification does not affect the convergence properties of the estimated parameters but instead improves the speed of convergence.