DescriptionSliding mode control is a form of variable structure control which is a powerful tool to cope with external disturbances and uncertainty. There are many applications of sliding mode control of weakly coupled system to absorption columns, catalytic crackers, chemical plants, chemical reactors, helicopters, satellites, flexible beams, cold-rolling mills, power systems, electrical circuits, computer/communication networks, etc. In this thesis, the problem of sliding mode control for systems, which are composed of two weakly coupled subsystems, is addressed. This thesis presents several methods to apply sliding mode control to linear discretetime weakly-coupled systems and di fferent approaches to decouple the sub-systems. The application of Utkin and Young's sliding mode control method on discrete-time weakly-coupled systems is studied in detail which is then compared with other control algorithms while emphasizing the importance of the decoupling technique in each case. It also presents the possibility of integrating two or more control strategies for a single system; one for each sub-system, depending upon the respective requirements and constraints. In this thesis, the eff ectiveness of the proposed methods is demonstrated through theory and simulation results.