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where beta and gamma are respectively the direction of the car and of the path in radians. The system has a pole in 0 and a pair of complex poles for
|k1| < sqrt(4 * w * k2 / alpha) = sqrt(4914 * k2)
which is true for any reasonable calibration of the controller. The pair of poles are
p = - alpha * v0^2 * k1 / 2w +- i * sqrt(4w * alpha * v0^2 * k_2 - alpha^2 * v_0^4 * k1^2) / 2w
DOCUMENTATION EXPANSION
These are likely to be expanded and moved on the main wiki page at some point.
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