reig (Robust Control Toolbox)

Real and ordered eigenstructure decomposition.

[xr,d] = reig(a)

[xr,d] = reig(a,Opt)

Description
Reig produces a "real" and "ordered" eigenstructure decomposition such that

where X_r is a set of "real" eigenvectors that span the same eigenspace as the complex ones. D is a real block diagonal matrix with real eigenvalue appearing as 1 x 1 block and/or complex eigenvalue a + jb appearing as a 2 x 2 block

Two types of ordering are available

Opt = 1 -- eigenvalues are ordered by real parts (default).
Opt = 2 -- eigenvalues are ordered by their magnitudes.

Algorithm
The kth real eigenvector pair xr(:, k:k+1) is

See Also
eig, cschur

perron, psv riccond