This paper considers the problem of designing a decentralized, high frequency, continuous-time periodic controller to simultaneously stabilize a class of two strongly interconnected LTI MIMO systems with or without decentralized fixed modes. The design is carried out by solving a pair of coupled linear simultaneous polynomial equations involving controller parameters via a generalized Sylvester matrix approach. The conditions which must be satisfied for a solution to exist are listed. The design approach is straightforward and linear algebraic in nature. An example is considered to illustrate the approach. (C) 2013 Elsevier Ltd. All rights reserved.