Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes

Change language to:
English - 日本語 - Português - Русский
Aide de Scilab >> Systèmes de Contrôle - CACSD > Calculs Matriciels > mucomp

mucomp

mu (structured singular value) calculation

Syntax

[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 Δ. The uncertainty Δ 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 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.

Examples

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)

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.

Report an issue
<< linmeq Calculs Matriciels ric_desc >>

Copyright (c) 2022-2023 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Mon Jan 03 14:33:06 CET 2022