Two days is not a long time [in] the scheme of things.  If they're satisfied that the chain of command is set after that short period, it suggests good short-term control.  Although we don't know yet, I'm guessing Jang Song Taek and Kim Jong Un are giving the orders and so far everyone is obeying. 

Jang Song Taek, Kim Jong Il's brother-in-law, who has been pulling the strings behind the scenes in recent months.  Martin continued:

They probably needed some time to figure out details like when the funeral would be held, what sort of announcement they should make to have the most positive impact on their own people and foreigners. 

Indeed, when Pyongyang did issue its official announcement, it looked carefully orchestrated.  See below:

And in this video, the masses of grieve in what appears to be part of a carefully orchestrated display. 

Michael Mazza, senior research associate who studies defense policy in the Asia-Pacific region and security on the Korean peninsula, said that the two-day wait period is hardly surprising.  They did the same thing when Kim Jong Il's father, Kim Il Sung, died in 1994.  He wrote by email:

Given North Korea’s secretive nature, it could take the time it needed to prepare its response without worrying about word of the death leaking out. 

"The real question now is whether that secretive nature may change for the better," he said. " Unfortunately, I wouldn’t bet on it."