I've only just come across this.
There's nothing particularly complex about time-triggered (TT) systems. What it means in practice is that you are creating systems using a single interrupt. This interrupt is usually linked to a timer overflow.
There are various different forms of TT system. In the simplest TT design, your system knows only when the next interrupt will occur. In other TT designs, your system knows when ALL future interrupts will occur.
A simple example: your system might have "ticks" (timer interrupts) every millisecond. All system operations would be controlled by this tick.
There is nothing mysterious about this approach to creating software (it has been used in safety-critical systems, such as aircraft, for many years). What is new is that some (enlightened) organisations are now using this approach in a much wider range of products (even very simple consumer products) in order to improve reliability and reduce development costs.
You mentioned RapidiTTy. This tool is produced by my company, and helps people to create systems with a TT architecture very quickly. The tool targets a range of ARM7 and Cortex-M3 microcontrollers (many more than those on your list), plus FPGAs, plus x86.
In a previous reply to your e-mail, it was suggested that my company exists simply to promote book sales. This is nonsense. In fact, if you are interested in TT architectures, you can download a large (1000- page) book on this topic for free from our WWW site (you don't even need to register).
Michael Pont TTE Systems Ltd