Given a sequence $Y_1, Y_2, \dots$ of i.i.d. matrices in $GL_n(\mathbb R)$, there is a theorem of Furstenberg and Kesten which says that if $\mathbb E(\logY_1)$ is finite, there exists a constant $\gamma$ (the Lyapunov exponent) such that $$\lim_{n\rightarrow\infty}\frac{1}{n}\logY_n\dots Y_1 = \gamma$$ There are also versions of central limit theorems for this scenario. I'm pretty sure this is also known in a more general case (e.g. suppose we have a sequence of matrices $Y_i$ of order 2, and I don't want to consider sequences of length $n$ in which $\dots Y_i Y_i\dots$ appears). I am wondering if anyone knows a good reference for theorems regarding Lyapunov exponents and central theorems in this case.

Random dynamical systems by Ludwig Arnold contains a thorough discussion of various multiplicative ergodic theorems (including the FurstenbergKesten result), but not the central limit theorems. As far as I remember, the case of stationary sequences of linear stochastic iterations is also included there. Edit. Concerning central limit theorems for products of random matrices, a quick search yields this reference. 


I had double checked, in the book "Products of Random Matrices With Applications to Schrodinger Operators" BOUGEROL Philippe, LACROIX Jean (chapter 5 of part 1) you will find Central Limit theorems even for markovian sequences. The FurstenbergKesten result generalizes as much as you like after Kingman's subaditive theorem. For this stuff, I like this notes http://www.mat.pucrio.br/~jairo/docs/trieste.pdf 


I believe the paper
available for free at http://www.preprint.impa.br/Shadows/SERIE_A/2005/384.html contains positivity results for the Lyapunov exponent over hyperbolic dynamical systems. Also the paper by C. Bonatti, X. GomezMont, and M. Viana cited as [7] in there should be of interest. I am not sure if they treat central limit theorems in these works. 

