Sufficient conditions for the robustness and convergence of P-type learning control algorithms for a class of time-varying, nonlinear systems are presented. We prove the uniform boundedness of the system state and the input control with respect to the existence of errors of initialization, measurement noises, and fluctuations of system dynamics. Furthermore, the system output converges uniformly to the desired one in absence of all disturbances. Finally, specialization of the results to linear systems are presented.