What you can use is a “controller”.
12 volt DC power supply to the controller, the LED strips connected and wireless connection via Zigbee or Z-Wave to your SmartThings hub.
Depending on your kind of LED strips you have white (even cool and warm white), RGB, RGBW & RGBWW (aka RGB-CCT).
Here an example: Gledopto Zigbee RGB controller
Some pictures of a controller:
Schematics:
