mucomp
mu (structured singular value) calculation
Calling Sequence
[BOUND, D, G] = mucomp(Z, K, T)
Arguments
Z
the complex n-by-n matrix for which the
structured singular value is to be computed
K
the vector of length m containing the block
dimensions of the structured uncertainty
\Delta. The uncertainty
\Delta is supposed to be a block
diagonal matrix.
T
the vector of length m indicating the type
of each uncertainty block. T(I) = 1 if the
corresponding block is real T(I) = 2 if the
corresponding block is complex.
BOUND
the upper bound on the structured singular value.
D, G
vectors of length n containing the diagonal
entries of the diagonal matrices D and G,
respectively, such that the matrix
Z'*diag(D)^2*Z + sqrt(-1)*(diag(G)*Z-Z'*diag(G)) -
bound^2*diag(D)^2
is negative
semidefinite.
Description
This function computes an upper bound on the structured
singular value for a given square complex matrix and given
block structure of the uncertainty.
The structured singular value \mu(Z) is
defined as the inverse of the norm of the smallest
uncertainty \Delta that makes
det(I-\Delta Z)=0. Here \Delta
is supposed to be a block diagonal matrix.
Examples
Used functions
This function is based on the Slicot routine AB13MD.
References
Fan, M.K.H., Tits, A.L., and Doyle, J.C.
Robustness in the presence of mixed parametric uncertainty
and unmodeled dynamics.
IEEE Trans. Automatic Control, vol. AC-36, 1991, pp. 25-38.
Slicot routine AB13MD.