Embedded computer systems use both off-the-shelf microprocessors and application-specific integrated circuits (ASICs) to implement specialized system functions. Examples include the electronic systems inside laser printers, cellular phones, microwave ovens, and an automobile anti-lock brake controller. it is a co-design problem - the hardware engine and application software architecture must be designed simultaneously. This text proposes techniques such as fixed-point iterations, phase adjustment, and separation analysis to efficiently estimate tight bounds on the delay required for a set of multi-rate processes preemptively scheduled on a real-time reactive distributed system. Based on the delay bounds, a gradient-search co-synthesis algorithm with techniques such as sensitivity analysis, priority prediction, and idle-processing elements elimination are developed to select the number and types of processing elements in a distributed engine, and determine the allocation and scheduling of processes to processing elements. This text describes techniques for the design of distributed embedded systems, which have arbitrary hardware and software topologies.