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dcontr

This fuction compute the C-Controlability, R-Controlability and I-Controlability, according with the next methods: flag=0: Direct method flag=1: Laurent expansion approach flag=2: kronecker-weistrauss canonical form

Calling Sequence

[nC]=dcontr(E,A,B,flag)
[nC,C_mat]=dcontr(E,A,B,flag)
[nC,C_mat,nR,R_mat]=dcontr(E,A,B,flag)
[nC,C_mat,nR,R_mat,nI, I_mat]=dcontr(E,A,B,flag)

Parameters

nC:

Rank of C controllability Matrix

C_mat:

C-controllability Matrices

nR:

Rank of R-Controllability matrix

nC:

R-controllability Matrix

nI:

Rank of I-Controllability matrix

C_mat:

I-Controllability matrix

R_mat:

R-Controllability matrix

E,A,B:

E, A and B matrices of descriptor system (E singular)

Examples

// This fuction compute the C-Controlability, R-Controlability and I-Controlability, according with the next methods
    // flag=0:  Direct method
    // flag=1:  Laurent expansion approach
    // flag=2:  kronecker-weistrauss canonical form
// For detailed information look into dcontr.sci in macros path

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];
// only rank of C- Controllability matrix with direct approach

[nC]=dcontr (E,A,B);
// Rank and matrices of C-controllability with direct aproach
[nC,C_mat]=dcontr (E,A,B,0);
// all ranks and matrices with method of laurent expansion approach
[nC,C_mat,nR,R_mat,nI,I_mat]=dcontr (E,A,B,1);

See also

Author

Bibliography

[1] Lewis, F. L. (1985). Fundamental, reachability, and observability matrices for discrete descriptor systems. IEE Transactions on Automatic Control 30(5), 502–505.

[2] Koumboulis, F. N. and Mertzios,(1999), B. G. on Kalman Controlability and Observability Criteria for Singular Systems Circuits Systems and Signals, 18, 269-290

[3] Duan, G.-R. Gao, D. Y. and Ogden, R. W. (Eds.) Analysis and Desing of Descriptor Linear Systems Springer, 2010

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