This paper studies, under state feedback policies, the H-infinity control design for large-scale jump linear systems where the form process admits strong and weak interactions. Through an analysis that covers both finite and infinite horizon cases and using averaging and aggregation techniques, an aggregate jump linear system of considerably smaller order has been obtained, along with a corresponding (compatible) cost function. This reduced-order (aggregate) problem is another piecewise-deterministic H-infinity control problem, and, on the basis of the solution of this problem, we obtain the asymptotic limit of the optimal performance level for the full-order system, as well as an approximate controller that can asymptotically achieve any desired performance level for the full-order system. A by-product of this analysis is a similar decomposition for the piecewise-deterministic linear-regulator problem.