Multiplexed stream cipher Consider the stream cipher that consists of 3 LFSRs, with the output of one coming being used to determine which of the other 2 is used that clock cycle.

Both the IV and the polynomials are secret.

Is this broken?  I know that the related shrinking generator is not, but needs buffering to avoid timing attacks.
Yes the multiplexing generator due to Jennings, and more advanced versions have been broken. I am assuming regular synchronous clocking of all 3 LFSRs in this answer.

The attacks mentioned are either correlation attacks or linear consistency attacks or a combination of the two. A reference which also cites earlier work is 

Optimal correlation attack on the multiplexer generator, Jovan Dj. Golic, Guglielmo Morgari, Information Processing Letters 109 (2009):838–841.