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riccati schur 389
riccati schur
Syntax
[x1,x2,stat,Heig min] = riccati schur(H,epp)
Parameter List
Inputs: H Hamiltonian matrix.
epp Tolerance for detecting proximity of eigenvalues to the jω
axis.
Outputs: x1,x2 Basis vectors for stable subspace. See description below.
stat Status flag.
0 Stable subspace calculated.
1 Failure to decompose into stable and
unstable subspaces.
Heig
min Minimum absolute value of the real part of the eigenvalues
of H.
Description
Solve the algebraic Riccati equation,
A
X + XA+XRX −Q =0,
by a real Schur decomposition method. The Hamiltonian, H, contains the Riccati
equation variables in the matrix,
H =
AR
Q−A
.
If H has no jω axis eigenvalues then there is an n dimensional (n = dim(A)) stable
subspace of H. The vector, [x
1
x
2
] spans that stable subspace and, if x
1
is invertible, the