This article presents a complete scheme for the integration and the development of multi-periodic critical embedded systems. A system is formally specified as a modular and hierarchical assembly of several locally mono-periodic synchronous functions into a globally multi-periodic synchronous system. To support this, we introduce a real-time software architecture description language, named \prelude, which is built upon the synchronous languages and which provides a high level of abstraction for describing the functional and the real-time architecture of a multi-periodic control system. A program is translated into a set of real-time tasks that can be executed on a monoprocessor real-time platform with an on-line priority-based scheduler such as Deadline-Monotonic or Earliest-Deadline-First. The compilation is formally proved correct, meaning that the generated code respects the real-time semantics of the original program (respect of periods, deadlines, release dates and precedences) as well as its functional semantics (respect of variable consumption).