Abstract: The article covers the study of generalized controllability of a discrete control system with a change in the dimensionality of the state vector. The con trollability problem is a key one in control theory. It characterizes the ability of the system to acquire the desired state at the final moment of time. It characterizes the ability of the system to acquire the desired state at the final moment of time. At the same time, the presence of restrictions on the control function expands the concept of controllability. For generalized controllability, the presence of ge ometric restrictions on the control function, as well as restrictions on the initial and final states of the system are characteristic features. In this case, partial controllability, complete controllability from a set of initial states, and complete controllability to a terminal set are distinguished. Partial controllability is charac terized by the ability of the system to transition to one of the states belonging to the terminal set. In the case of complete controllability, the system is able to get to one of the points of the terminal set from any point in the region of initial con ditions. Complete controllability to the terminal set is characterized by the ability of the control system to go to each point of the set of final states from at least one position belonging to the set of initial conditions. The proposed article con tinues the study of generalized controllability of discrete systems in the case when the dimensionality of the state vector changes. Mathematical models of processes with a change in the dimensionality of the state vector have been studied little, they are associated with the representation of the system in a struc tural form. In the process of functioning of a system consisting of subsystems, subsystems may disappear, or new ones may appear. In particular, this feature is present in mathematical models of technological processes. In the work, for each type of generalized controllability for a linear control system with a change in the dimensionality of the state vector, the controllability function is defined and the controllability criteria are substantiated. The justification essentially uses the apparatus of convex analysis and the properties of the reachability set of a linear control system. At the same time, for constraints on control and state in the form of balls, conditions were found that the radii of such balls must satisfy for each type of generalized controllability.