Solving Stein equations in QT format

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The theory for the solution of Stein equations is related with the one for solving Lyapunov and Sylvester equations, which can be done with the command cqtlyap.

A Stein equation has the form $AXB + X + C = 0$, for given matrices $A,B,C$. If the latter are $\mathcal{QT}$ matrices and the product of any two elements in the spectra of $A$ and $B$ is always smaller than $1 - \epsilon$ for some $\epsilon > 0$, then the solution $X$ is representable in $\mathcal{QT}$ format as well.

Contents

Syntax

Example

A = cqt([ .5 .2 ], [.5 .2 ]);
B = A;
C = cqt(1, 1);

X = cqtstein(A, B, C);

norm(A*X*B + X + C) / norm(C)

ans =

   8.3250e-12