Multi-input Controllable Canonical Form

This function computes the frobenius transformation T for a multi-input state representation (A,B) such that the transformed system (T*A*inv(T),T*B) is in the multi-input controllable canonical form.

Refer : D. G. Luenberger, "Canonical forms for linear multivariable systems", IEEE Trans. Auto. Contr., Vol. 12, pp. 290-292, 1967.

The format of the function is
[T,Ad,Bd,ni]=MI_CTRB(A,B)
The function takes the following inputs
A - The state matrix
B - The input matrix
and gives output
T - The generalized frobenius transformation matrix.
Ad,Bd - The state and input matrices of the transformed system.
ni - A vector describing the extent of controllability of the system with each input (also termed as controllability index).

Note : mu=max(ni) would give the controllability index of the system with all inputs. i.e., the system is never controllable with ni(j)<mu for all j.