Continuously on power strip with short cycle ON/OFF switch?
A 555 timer could do the job, but a small microcontroller with a stable time base, zero crossing detector, and internal timers would allow for more accuracy and a lower cost AC relay (vs. solid state relay) to be used.

A small AC coupled power supply is used to generated the 5V needed.  The microcontroller will also monitor the AC supply with a "zero crossing detector" to know when to close the main AC relay (closing at 0V prevents arcing, allowing a lower cost relay to be used).

Microchips 8 pin device PIC12F1501 comes to mind.