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See the recommended documentation of this function
st_ility
stabilizability test
Syntax
[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])
Arguments
- 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 stabilizable 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
).
Examples
See also
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