Theory and Modern Applications
Table 1 Several linear matrix equations
From: Matrix iteration algorithms for solving the generalized Lyapunov matrix equation
\(AX + XA^{T}+C=0 \) | continuous-time Lyapunov matrix equation |
\(AXD^{T}+DXA^{T}+C=0\) | generalized continuous-time Lyapunov matrix equation |
\(A^{T}XA-D^{T}XD+C=0\) | generalized discrete-time Lyapunov matrix equation |
AX − XD + C = 0 | continuous-time Sylvester matrix equation |
\(AXD^{T}-X+C=0\) | discrete-time Sylvester matrix equation |