This paper is concerned with a global H-infinity control problem for a class of interconnected non-linear systems. We first consider a fairly general class of large-scale non-linear systems with strong non-linear interconnections. It is shown that the decentralized H-infinity control problem for the system can be converted into the centralized control problems associated with a set of auxiliary systems. The solutions to the latter problems in general rely on solutions of their associated Hamilton-Jacobi-Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then consider a global decentralized almost disturbance decoupling problem (DADDP) and a global decentralized inverse H-infinity control problem (DIHCP) for a class of interconnected systems with lower triangular structure. The DADDP is concerned with the design of decentralized control laws that achieve an arbitrarily small L-2-gain from the disturbance input to the controlled output. The DIHCP involves seeking not only control laws but also state-dependent weights of the control inputs such that the associated global decentralized control problem is solvable. It is shown that the solutions to both the DADDP and DIHCP can be obtained via a recursive design technique.