This paper presents a robust decentralized model predictive control scheme for a class of discrete-time interconnected systems subject to state and input constraints. Each subsystem is composed of a nominal LTI part and an additive time-varying perturbation function which presents the interconnections and is generally uncertain and nonlinear, but it satisfies a quadratic bound. Using the dual-mode MPC stability theory and Lyapunov theory for discrete-time systems, a sufficient condition is constructed for synthesizing the decentralized MPC’s stabilizing components; i.e. the local terminal cost function and the corresponding terminal set. To guarantee robust asymptotic stability, sufficient conditions for designing MPC stabilizing components are characterized in the form of an LMI optimization problem. The proposed control approach is applied to a system composed of five coupled inverted pendulums, which is a typical interconnected system, in a decentralized fashion. Simulation results show that the proposed robust MPC scheme is quite effective and has a remarkable performance.