Generalized eigenvalue problem A x = s B x, QZ decomposition. There are three ways to call this function:
lambda = qz(A,B)
Computes the generalized eigenvalues of (A - s B).
[AA, BB, Q, Z, V, W, lambda] = qz (A, B)
Computes qz decomposition, generalized eigenvectors, and generalized eigenvalues of (A - sB) with Q and Z orthogonal (unitary)= I
[AA,BB,Z{, lambda}] = qz(A,B,opt)
As in form [2], but allows ordering of generalized eigenpairs for (e.g.) solution of discrete time algebraic Riccati equations. Form 3 is not available for complex matrices, and does not compute the generalized eigenvectors V, W, nor the orthogonal matrix Q.
- opt
- for ordering eigenvalues of the GEP pencil. The leading block of the revised pencil contains all eigenvalues that satisfy:
"N"
- = unordered (default)
"S"
- = small: leading block has all |lambda| <=1
"B"
- = big: leading block has all |lambda| >= 1
"-"
- = negative real part: leading block has all eigenvalues in the open left half-plane
"+"
- = nonnegative real part: leading block has all eigenvalues in the closed right half-plane
Note: qz performs permutation balancing, but not scaling (see balance). Order of output arguments was selected for compatibility with MATLAB