Kinematic Collision

Does anyone know any good paper on handling collision between kinematic 
objects & static shapes, I dont know the correct term but I think I'm 
aiming at the collision model used in almost all games today, i.e. a 
none-physical solution with bump & slide. My current implementation is 
almost working but I have a couple of question marks I need to sort out, 
mainly stability, performance and slope/stepping.

The way I'm doing it now is a recursive collision response, performing 
the following steps.

While iterations are not to high

    Step 1:
    If our current position is our target position we can end, otherwise 
do a capsulesweep from our current position to our target position + a 
small bias, if no collision is reported we can end otherwise continue to 
step 2

    Step 2:
    Calculate the closest position before the collision point and offset 
with the bias, Set our current position to this location.

   * NewPosition = Position + Direction * (DistanceToImpact - Bias)

    Step 3:
    Find the vector from the new position and the target location and 
retrieve the reflection/tangent components. Set new target position to 
the new current position and add both components scaled by a
    bounce/friction value [0, 1] to it..

    * NormalMotion = NormalComponent * Bounce
    * TangentMotion = TangentComponent * Friction
    * NewTargetPosition = NewPosition + NormalMotion + TangentMotion

    Repeat Step 1:

This algo is not very stable, sometimes when I calculate the position 
right before the impact point it will closer then my bias, resulting in 
weird behavior, but I'm unsure how this can happen since I make sure to 
include the bias during the offset, and I have also tried setting the 
collision point with 2x bias as offset.

I'm also worried that it will fail to solve the collision before running 
out of iterations, but building the level with some constraints is maybe 
enough promise to never allow this to happen? How are you guys doing 
this? I have also peaked on the NxCharacter source and it looks ALOT 
more advanced then my simple algo and I take it like I'm missing to 
perform some important steps?

I also whonder how stepping & sloping could be handled, right now I was 
hoping that the capsule hemispheres would automatically solve this issue 
by giving me tangential motion for objects small enough, causing 
automatic stepping, but so far no luck, but this is probably due to the 
bias issue.

Atleast the capsule cannot interpenetrate objects, but I need to be able 
to handle slops & stairs, any link to a good paper or personal 
experience/knowledge is highly appreciated.

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