The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems.[1][2]
In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is
where is a Hermitian matrix and is the conjugate transpose of , while the continuous-time Lyapunov equation is
.
^Parks, P. C. (1992-01-01). "A. M. Lyapunov's stability theory—100 years on *". IMA Journal of Mathematical Control and Information. 9 (4): 275–303. doi:10.1093/imamci/9.4.275. ISSN 0265-0754.
^Simoncini, V. (2016-01-01). "Computational Methods for Linear Matrix Equations". SIAM Review. 58 (3): 377–441. doi:10.1137/130912839. hdl:11585/586011. ISSN 0036-1445.
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