In this paper, a decentralized iterative leing control strategy is embedded into the procedure of hierarchical steady-state optimization for a class of linear large-scale industrial processes which consists of a number of subsystems. The task of the leing controller for each subsystem is to iteratively generate a sequence of upgraded control inputs to take responsibilities of a sequential step functional control signals with distinct scales which are determined by the local decision-making units in the two-layer hierarchical steady-state optimization processing. The objective of the designated strategy is to consecutively improve the transient performance of the system. By means of the generalized Young inequality of convolution integral, the convergence of the leing algorithm is analyzed in the sense of Lebesgue-p norm. It is shown that the inherent feature of system such as the multi-dimensionality and the interaction may influence the convergence of the non-repetitive leing rule. Numerical simulations illustrate the effectiveness of the proposed control scheme and the validity of the conclusion.