Constrained Matrix Sylvester Equations

TitleConstrained Matrix Sylvester Equations
Publication TypeJournal Articles
Year of Publication1992
AuthorsBarlow JB, Monahemi MM, O'Leary DP
JournalSIAM Journal on Matrix Analysis and Applications
Pagination1 - 9
Date Published1992///
Keywordsloop transfer recovery, matrix Liapunov equation, Sylvester operator

The problem of finding matrices $L$ and $T$ satisfying $TA - FT = LC$ and $TB = 0$ is considered. Existence conditions for the solution are established and an algorithm for computing the solution is derived. Conditions under which the matrix $[C^T ,T^T ]$ is full rank are also discussed. The problem arises in control theory in the design of reduced-order observers that achieve loop transfer recovery.