Algebraic Riccati Equation Solver

Solves a common algebraic Riccati equation using Schur decomposition.

This function solves an algebraic Riccati equation of the form:

A'*X + X*A' - X*G*X + Q = 0,

where A, G, and Q are given and X is the symmetric solution. All terms are real nxn matrices and G and Q are positive semi-definite.

A common use of this equation is to solve for the optimal feedback gain of a linear system, in which case

G = B*R^-1*B' and K = R^-1*B'*X.

See http://en.wikipedia.org/wiki/Linear-quadratic_regulator for more detail. Based on the solution method of http://dspace.mit.edu/handle/1721.1/1301.