Explicit and analytical solutions to Sylvester algebraic matrix equations

Abstract

Based on a recently proposed explicit and complete parametric solution to the generalized Sylvester matrix equation in the form of AV+EVF=BW, explicit and analytical solutions to the Sylvester matrix equations AV-EVF=W and AV-VF=W are derived. Cases of multiple solutions are also treated. These solutions are in simple and compact forms, and may have important applications in control systems theory.