The object of research is digital systems of decentralized control of quasi-stationary multi-connected processes taking into account structural disturbances. It was determined that the promising development of decentralized control of multi-connected processes is research related to considering the possibility of its application for real situations of partial disruption of interconnections between subsystems in multidimensional stochastic systems. Such studies are not sufficiently developed today, therefore the topic of the proposed work should be considered relevant from the theoretical and applied points of view. The problem of decentralized management of multi-connected stochastic objects is formalized, taking into account the internal relationships between their local subsystems of the system. A method of decentralization of a multi-connected system is proposed, the advantage of which is the use of simple computational procedures of transformation and permutation of matrix elements of the global model. The concept of c-robustness of a multi-connected dynamic system is introduced, which guarantees its asymptotic stability and suboptimality in the event of structural disturbances. Methods of robust decentralized control are proposed for cases of explicit and implicit tasks of interconnections between local subsystems. The proposed methods have a certain advantage in comparison with the method of local control coordination, which consists in increasing the efficiency of decentralized control with a guaranteed level of suboptimality. Experimental modeling of the considered method for models of multi-connected chemical-technological systems describing the relationship between the input and output parameters of the processes was carried out. During the simulation, the global system was decomposed into 4 local subsystems. Modeling of the task of decentralized management was also carried out according to the well-known method of coordination, based on finding the values of uncertain multipliers. A comparative analysis of the results obtained using this standard method and the proposed robust methods shows the superiority of the latter.