lyap — solution of the lyapunov equation


\begin{rail} Lyapunov : 'lyap' '(' Matrix ',' ( () \vert Matrix) ',' Matrix ')' ; \end{rail}
lyap is used to solve the general form of the Sylvester equation, and its special form in the Lyapunov equation. It is very similar to the sylv function, except that the arguments need not be upper triangular. Given the first matrix argument is A, the second matrix argument is B, and the third matrix argument is C, lyap solves

Ax + xB = - C

for x. If there are only two arguments, it is assumed B = AT, and the Lyapunov equation is solved. Note that in sylv, you leave out the comma and the argument — lyap requires both commas. $\Longrightarrow$ This is not an built-in function. This function is normally loaded on start-up from the lyap.r file in the standard rlib directory. Use of the -r option, incorrectly setting the RLAB_LIB_DIR environmental variable, or modifying lyap.r may make this function unavailable.
Subsections