mu (structured singular value) calculation
[BOUND, D, G] = mucomp(Z, K, T)
the complex n-by-n matrix for which the structured singular value is to be computed
the vector of length m containing the block dimensions of the structured uncertainty Δ. The uncertainty Δ is supposed to be a block diagonal matrix.
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.
the upper bound on the structured singular value.
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.
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 μ(Z) is defined as the inverse of the norm of the smallest
uncertainty Δ that makes det(I- ΔZ)=0
. Here Δ is supposed to be a
block diagonal matrix.
K=[1,1,2,1,1]; T=[1,1,2,2,2]; Z=[-1+%i*6, 2-%i*3, 3+%i*8, 3+%i*8,-5-%i*9,-6+%i*2; 4+%i*2,-2+%i*5,-6-%i*7,-4+%i*11,8-%i*7, 12-%i; 5-%i*4,-4-%i*8, 1-%i*3,-6+%i*14,2-%i*5, 4+%i*16; -1+%i*6, 2-%i*3, 3+%i*8, 3+%i*8,-5-%i*9,-6+%i*2; 4+%i*2,-2+%i*5,-6-%i*7,-4+%i*11,8-%i*7, 12-%i; 5-%i*4,-4-%i*8, 1-%i*3,-6+%i*14,2-%i*5, 4+%i*16]; [BOUND, D, G] = mucomp(Z, K, T) spec(Z'*(diag(D)^2)*Z + %i*(diag(G)*Z-Z'*diag(G)) - BOUND^2*diag(D)^2) | ![]() | ![]() |
This function is based on the Slicot routine AB13MD.
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.