Transverse mode coupling (TMC) instability  is one of the major limitations of a single bunch current in large storage rings. This paper is devoted to a theoretical analysis of the effect of transverse feedback systems on TMC thresholds. It presents a space-time formalism for a hollow beam model and time-independent collective interaction. Then, in the framework of a simplified model, the principle of eliminating the TMC by means of a special transverse feedback system is outlined. This approach is then generalized in the form of an algorithm.