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CONTR Scilab Group Scilab Function CONTR
NAME
contr - controllability, controllable subspace
CALLING SEQUENCE
[n [,U]]=contr(A,B [,tol])
[A1,B1,U,ind]=contr(A,B [,tol])
PARAMETERS
A, B : real matrices
tol : may be the constant rtol or the 2 vector [rtol atol]
rtol :tolerance used when evaluating ranks (QR factorizations).
atol :absolute tolerance (the B matrix is assumed to be 0 if
norm(B)<atol)
n : dimension of controllable subspace.
U : orthogonal change of basis which puts (A,B) in canonical form.
A1 : block Hessenberg matrix
B1 : is U'*B.
ind : vector associated with controllability indices (dimensions of
subspaces B, B+A*B,...=ind(1),ind(1)+ind(2),...)
DESCRIPTION
[n,[U]]=contr(A,B,[tol]) gives the controllable form of an (A,B)
pair.(dx/dt = A x + B u or x(n+1) = A x(n) +b u(n)). The n first columns
of U make a basis for the controllable subspace.
If V=U(:,1:n), then V'*A*V and V'*B give the controllable part of the
(A,B) pair.
[A1,B1,U,ind]=contr(A,B) returns the Hessenberg controllable form of
(A,B).
EXAMPLE
W=ssrand(2,3,5,list('co',3)); //cont. subspace has dim 3.
A=W("A");B=W("B");
[n,U]=contr(A,B);n
A1=U'*A*U;
spec(A1(n+1:$,n+1:$)) //uncontrollable modes
spec(A+B*rand(3,5))
SEE ALSO
canon, cont_mat, unobs, stabil
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