LOCAL STABILITY ANALYSIS FOR A CLASS OF ADAPTIVE SYSTEMS.

An analysis of adaptive systems is presented where a local L infinity -stability is ensured under a persistent excitation condition. The stability analysis involves establishing the exponential stability of a differential equation which arises in the study of most adaptive systems. Although the connection between exponential stability and persistent excitation is known, it is important to obtain specific formulas for the rates and gains involved. However, L infinity -stability can be obtained by using a nonlinear adaptation gain, i. e. , theta = Yh(z,e). For example, h(z,e) can arise from using a dead zone, leakage, or normalization. Such schemes can be incorporated in the general framework presented but require further analysis in order to obtain explicit signal bounds.