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st_ility(1) Scilab Function st_ility(1)
NAME
st_ility - stabilizability test
CALLING SEQUENCE
[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])
PARAMETERS
Sl : syslin list (linear system)
ns : integer (dimension of stabilizable subspace)
nc : integer (dimension of controllable subspace nc <= ns)
U : basis such that its ns (resp. nc) first components span the
stabilizable (resp. controllable) subspace
Slo : a linear system (syslin list)
tol : threshold for controllability detection (see contr)
DESCRIPTION
Slo=( U'*A*U, U'*B, C*U, D, U'*x0 ) (syslin list) displays the stabiliz-
able form of Sl. Stabilizability means ns=nx (dim. of A matrix).
[*,*,*] [*]
U'*A*U = [0,*,*] U'*B = [0]
[0,0,*] [0]
where (A11,B1) (dim(A11)= nc) is controllable and A22 (dim(A22)=ns-nc) is
stable. "Stable" means real part of eigenvalues negative for a continuous
linear system, and magnitude of eigenvalues lower than one for a discrete-
time system (as defined by syslin).
EXAMPLE
A=diag([0.9,-2,3]);B=[0;0;1];Sl=syslin('c',A,B,[]);
[ns,nc,U]=st_ility(Sl);
U'*A*U
U'*B
[ns,nc,U]=st_ility(syslin('d',A,B,[]));
U'*A*U
U'*B
SEE ALSO
dt_ility, contr, stabil, ssrand
AUTHOR
S. Steer INRIA 1988
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