DiscreteLyapunovSolve
DiscreteLyapunovSolve[a, c] finds the numeric solution x of the discrete matrix equation a.x.a† - x = c.
DiscreteLyapunovSolve[a, b, c] solves a.x.b† - x = c.
DiscreteLyapunovSolve[{a, d}, c] solves a.x.a† - d.x.d† = c.
DiscreteLyapunovSolve[{a, d}, {b, e}, c] solves a.x.b† - d.x.e† = c.
Examples
Solve discrete Lyapunov equation:
DiscreteLyapunovSolve[{{0.5}}, {{1}}]Please visit the official Wolfram Language Reference for more details.