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We study in this paper solutions to several kinds of linear bimatrixequations arising from pole assignment and stability analysis of complex-valuedlinear systems, which have several potential applications in control theory,particularly, can be used to model second-order linear systems in a very densemanner. These linear bimatrix equations include generalized Sylvester bimatrixequations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunovbimatrix equations. Complete and explicit solutions are provided in terms ofthe bimatrices that are coefficients of the equations/systems. The obtainedsolutions are then used to solve the full state feedback pole assignmentproblem for complex-valued linear system. For a special case of complex-valuedlinear systems, the so-called antilinear system, the solutions are also used tosolve the so-called anti-preserving (the closed-loop system is still anantilinear system) and normalization (the closed-loop system is a normal linearsystem) problems. Second-order linear systems, particularly, the spacecraftrendezvous control system, are used to demonstrate the obtained theoreticalresults.

Solutions to Linear Bimatrix Equations with Applications to Pole Assignment of Complex-Valued Linear Systems