This paper addresses the application of convergence rules of gradient-type discrete algorithms to discrete adaptive control algorithms for linear time-invariant systems, which are based on Lyapunov's – like functions, in order to improve the transient performances based on fast adaptation. In particular, the adaptation covergence is increased as a generalized or filtered error increases through the application of Armijo rule for regulating the decrease of each Lyapunov's-like function on which the particular adaptation algorithm is based. The proposed scheme can be implemented with minor modifications in systems subject to unmodelled dynamics if some weak knowledge on such a dynamics is available consisting of upper-bounds of the dimension and norm of the unmodelled parameter vector.