This article proposes four sufficient conditions to determine the convergent learning parameters in iterative learning control of linear batch processes. These conditions are established in frequency domain with transfer functions of elementary linear learning functions of P-, D-, PD- and PID-Type, instead of their state space models as usual. Hence, they can overcome all conservative difficulties occurred by using conditions created in time domain. To obtain these conditions in frequency domain, first an overall sufficient condition belonging to time domain is created, and then realized it particularity in frequency domain for four different linear learning functions by using their transfer function. The obtained conditions in frequency domain are expressed in algebraic inequality of matrix norm, so they are very convenient in use. To illustrate the applicable ability of proposed conditions in various practical applications some numerical simulations had been carried out in the paper. Obtained simulation results authenticated the advantage of these conditions.
