Controllability, Observability and Stabilization of a Class of Matrix Linear Systems

In this paper we consider the controllability and observability properties of the matrix linear system X = AX +X d + BU,Y = CX where A,srf,B and C are some known matrices. It is shown that such system is controllable and observable if and only if the corresponding linear system X = AX + BU,Y = CX is controllable and observable, respectively. Some explicit conditions are established. Furthermore, stabilization of such matrix linear system by state feedback is considered.