The paper is devoted to plasma shape, current, vertical position, and vertical speed control systems in T-15 tokamak. Brief definitions of the control problem statement and T-15 tokamak itself as a plant under control are given. A cascade plasma shape and current control system is designed using control channel decoupling matrixes in the inner loop and the H∞ controller in the outer loop obtained by means of H∞ optimization theory based on the normalized coprime factorization approach of a plant model. Proportional and H∞ controllers are used to stabilize the plasma vertical position as well as the plasma vertical speed. The first one was applied to plasma-physics DINA code. During simulations some essential difference between linear DINA-L model and plasma-physics DINA code itself was discovered which led to the conclusion to apply an identification procedure on DINA code to get more accurate linear models for the feedback controller design.