Which algorithm is used in the isproper function to reduce the number of states?

The isproper function in Matlab can transform a descriptor state space model:

E*Dx = A*x + B*u

y=C*x + D*u

with a singular Matrix E into an equivalent model with fewer states and a non-singular E matrix. How is this transformation from a DAE to an ODE achieved? Which algorithm is used?

Thanks for considering my question.

Answer 1

[Yoke Peng Leong]

The specific implementation is proprietary. However, at high level, it involves eliminating pole/zero cancellations at infinity using a form of staircase algorithm.