A sound field control approach is investigated for recording a primary sound field and synthesizing it at a secondary field without exterior radiation using circular double-layer arrays of microphones and loudspeakers. Although the conventional least-squares (LS) and generalized singular value decomposition (GSVD) approaches are based on numerical solutions and control the discretized interior and exterior sound pressures, this paper provides a mode-matching-based analytical method with circular double-layer receiver and source. The primary sound field cylindrical harmonic spectrum is analytically estimated from the recorded sound pressures without forbidden frequencies, and the driving signals of the loudspeakers for synthesizing it are analytically derived without interior and exterior control points. Computer simulations demonstrate the effectiveness of the proposed analytical formulation with circular double-layer arrays of microphones and loudspeakers. Compared to the conventional numerical LS and GSVD approaches, the interior sound field synthesis is more accurate and the exterior sound propagation is more effective in the proposed method under both free-field and reverberant conditions.