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 The LQRTrees software toolbox for MATLAB is currently being alphatested. A public beta release is expected shortly.
The most difficult part of the LQRTrees algorithm to implement is the trajectory verification (e.g., computing the funnels). You can find the technical details in the following paper, and a standalone MATLAB example in the supplemental zip file.

Mark M. Tobenkin, Ian R. Manchester, and Russ Tedrake.
Invariant funnels around trajectories using sumofsquares
programming.
Proceedings of the 18th IFAC World Congress, extended version
available online: arXiv:1010.3013 [math.DS], 2011.
MATLAB example in supplemental zip file [ arXiv 
http ]
[ .zip ]
