That's where I ended up too...
When I looked I discovered one or two older devices actually described as "trigger controlled AC outlets"...
But they tended to be bulky and expensive (like the Xantech AC1)...
Many of the older ones also use mechanical relays...
And, while they are built like tanks, the relay is driven directly by the input, which can cause problems for modern solid state trigger control circuitry...
Relay coils require a significant amount of current to drive - some as much as 100 mA or even more.
Relay coils also generate a pulse of back-EMF voltage when de-energized; the device should include snubbers to suppress this but some seem not to.
However there seem to be a lot of newer devices designed to be used for "home automation" or "projects"... and controlled by gadgets like the Raspberry Pi and Arduino...
These have more sophisticated circuitry - including an opto-isolator on the input.
So, instead of powering a relay directly, the input signal merely lights an LED.
Most of these will operate over a very wide range of voltages - some as wide as 5V - 48V.
And they draw very little current and so are very easy to drive by virtually any trigger output.
I've seen the outlet strips that turn on when they "sense" that a device connected to one special outlet is powered on...
They seem like they might be a reasonable solution...
But, while I've never personally used one, I have heard that
some of them can be excessively "fussy"...
For example, I heard of one case where a preamp plugged into the "sensing outlet" didn't draw enough power to turn on the other outlets.
And, alternately, if you leave your preamp or processor in Standby, it may never draw little enough current for the main outlets to switch
off.
It's also worth mentioning that the switched outlet Geebo linked (which is the one I have) has both normally-on and normally-off outlets.
(So, if you wanted to, you could even have a room lamp that switches off when the amps turn on... so the lights dim when the music starts... and turn back on when you turn the music off
.)