NEW CONVERGENCE ANALYSIS IN ADAPTIVE-CONTROL - CONVERGENCE ANALYSIS WITHOUT THE BARBALAT LEMMA

Convergence of the state error e to zero in adaptive systems is shown using the existence and uniqueness of solution and the existence of a Lyapunov function in which the adaptation laws are constructed. Result s in the paper are general in the sense that it is applicable to a bro ad class of adaptive systems of a linear/nonlinear, time-varying or di stributed-parameter systems. Since the approach taken in the paper doe s not require the boundedness of the derivative of the state error e f or all t greater than or equal to 0, it is particularly useful in the adaptive control of infinite dimensional systems.