Abstract : We focus on the question of real-time computation for optimal distributed ﬁltering or control applicable to MEMS Arrays. We present an algorithm for the realization of a linear operator solution to a functional equation through its application to a Lyapunov operatorial equation associated to the heat equation in one dimension. It is based on the diffusive realization, and turns to be well suited for ﬁned grained parallel computer architecture as Field Programmable Gate Arrays (FPGA). An effective FPGA implementation has been successfully carried out. Here, we report the main implementation steps and the ﬁnal measured performances.