Simplification of the Lyapunov matrix equation A_{T}PA - P = -Q
Stephen Mark Barnett · IEEE Transactions on Automatic Control · 1974
It is shown that in solving for the symmetric matrixPthe number of linear equations and unknowns can be reduced from\frac{1}{2}n(n + 1)to\frac{1}{2}n(n - 1)by introducing a skew-symmetric matrix. This corresponds to an earlier result for the equationA_{1}^{T}P_{1} + P_{1}A = -Q.