riccati schur 389
riccati schur
Syntax
[x1,x2,stat,Heig min] = riccati schur(H,epp)
Parameter Li st
Inputs: H Hamiltonian matrix.
epp Tolerance for detecting proximityof eigenvalues to the jω
axis.
Outputs: x1,x2 Basis vectors for stable subspace. See description below.
stat Statusflag.
0 Stable subspace calculated.
1 Failure to decompose into stable and
unstable subspaces.
Heig min Minimum absolute valueof the realpart of the eigenvalues
of H.
Description
Solve the algebraic Riccati equation,
A0X+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
0
.
If Hhas no jω axis eigenvalues then there is an ndimensional (n=dim(A)) stable
subspace of H. The vector, [x1x2] spans that stable subspace and, if x1is invertible, the