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DeCaToKi >> en_US > qrrse

qrrse

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).

Calling Sequence

[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)

Parameters

E, A, B, C:

Matrices of descriptor system, E singular and pair (E, A) not necessarily regular.

F,G:

Descriptor system matrices, when unknowed input are considered like in Darouach, (1995) [1]

Ee, Ae, Ae1, Be, Be1, Ce:

Matrices of the qr r.s.e system

Fe, Fe1, De:

Matrices of equivalent qr r.s.e system when unknown inputs are considered [2]

Description

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

Examples

// Descriptor system
E=[1 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0];
A=[-0.8775 0 0.526 -0.0274;
    -5.8500  -0.5 0.1481 0.0026; 
    0      0.5   -1     0.2;
    0      2.6522  -0.274  -2];
B=[ 0 0; -0.0856  0.01; 0 0; 0 1];
C=[1 1 0 1; 0 0 1 1;0 0 1 0];

// Compute the Kronecker-Weistrauss r.s.e of (E,A),
 [Ee, Ae, Ae1, Be, Be1, Ce]=qrrse(E,A,B,C)
// QR r.s.e of  hole descriptor system with unknown inputs
F=[-1 0 0 0]';
G=[0 0]';

[Ee, Ae, Ae1, Be, Be1, Ce,Fe,Fe1,De]=qrrse(E,A,B,C,F,G)

See also

Authors

Bibliography

[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

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