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darobsv96

This function compute the gains for recuded order Darouach observer with unknown inputs [1]

Calling Sequence

[Pi, L1, L2, H, M, N,C11,C12]=darobsv96(E,A,B,C,F,G)

Parameters

E, A, B,C:

Continuos matrices of descriptor system. E singular

F, G:

Unknown input matrices of the descriptor system

Pi, L1, L2, H, M, N:

Gains matrices of the observer

C11 and C12

Auxiliar matrices for simulation, this can be obtained from qrrse transformation

Description

Given a Descriptor system in the form
dxEdt=A x(t) + B u(t) +F d (t)
y   =C x(t) + D u(t) +G d(t)
if the conditions in [1] are satisfied, then exist a reduced order observer
dzdt=Pi z(t) + L1 y1(t) + L2 y2(t) H u(t)
xe=Mz(t) + N y2(t)
xe is the stiamted output, u is the input.
and y1(t)=C11 x(t) + d1(t)  y2(t)=C12 x(t)
For more information consult the reference. Observability conditions are tested inside the function

Examples

Descriptor System
E=[1 0 0 0 ; 0 1 0 0; 0 0 1 0; 0 0 0 0];
A=[-1 1 0 0 ; -1 0 0 1; 0 -1 -1 0; 0 0 0 1];
B=[1 0 0 1]';
C=[1 0 0 0; 0 0 1 1];

F=[-1 0 0 0]';
G=[0 0]';
// Observer Gains

[Pi, L1, L2, H, M, N,C11,C12]=darobsv96(E,A,B,C,F,G);

See also

Author

Bibliography

[1] M. Darouach and M. Boutayeb, (1995). Design of Observer for Descriptor Form. IEEE Transactions on Automatic Control. Vol. 70, pp. 1323-1327

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