this function compute the QR restricted system equivalence of a descriptor system l (E, A,B,C) or with unknown input (E, A, B, C,F,G).
[Ee, Ae, Ae1, Be, Be1, Ce]=qrrse(E,A,B,C) [Ee, Ae, Ae1, Be, Be1, Ce,Fe,Fe1,De]=qrrse(E,A,B,C,F,G)
Matrices of descriptor system, E singular and pair (E, A) not necessarily regular.
Descriptor system matrices, when unknowed input are considered like in Darouach, (1995) [1]
Matrices of the qr r.s.e system
Matrices of equivalent qr r.s.e system when unknown inputs are considered [2]
QR restricted system equivalence of descriptor systems, considering restriccions in [1] and [2], if there exist a P matrix such that
PE=[E2 0]*
PA=[Ae Ae1]*
PB=[Be1 Be2]*
Ce=[Ae C]*
and if unknowed inputs are considered [2], then
Fe=[Fe Fe1]
De=[Fe G]
* indicates the transpose. For more deatiled help, see the qrrse.sci file in macros path
[1] Darouach, M. and Boutayeb, (1995). Design of Observers for Descriptor Systems. IEE Transactions on Automatic Control. Vol. 40, pp. 1323-1327
[2] Darouach, M. , M. Zasadzinski and M. Hayar, (1996). Reduced-order observer design for descriptor systems with unknown inputs.IEEE Transactions on Automatic Control. Vol 41, Num. 7, pp. 1068-1072