Hello,
I'm using this ASL shield for my stairs project. Arduino extantion shield,stairs automation
I'm using two power sources to power up arduino ASL and 20 LED strips (1meter length each). 10 strips on first power source and 10 on another.
Maybe someone have advice why only half of LED strips are working? LED strips works only from that power source where arduino ASL shield is connected...
You must have posted the wrong diagram, because the one you posted has only one power supply and one led strip.
Here is a link to your shield so that others don't have to copy & paste the address you posted into their browsers.
pufiks:
Maybe someone have advice why only half of LED strips are working? LED strips works only from that power source where Arduino ASL shield is connected...
That would strongly suggest a wiring error. If you provide a proper diagram of what you have done, we might be able to help. Obviously you have tested the output voltage of each of these supplies. 
PaulRB:
Here is a link to your shield so that others don't have to copy & paste the address you posted into their browsers.
Interesting board. I have been unable to locate a proper schematic for it, seems to be some sort of "trade secret", but the Si2302DS FETs it uses appear to be an excellent choice giving more capability than TPIC6595s. I can think of some other good uses for them (organ pipe drivers).
Unfortunately, it appears to lack a proper regulator to provide 5 V for the Arduino. And I cannot see how it would provide individual dimming for the treads without some convoluted (softPWM) code.
Attaching quick sketch