Rami, Mustapha AitChen, XiMoore, JohnZhou, Xun2015-12-102015-12-100018-9286http://hdl.handle.net/1885/69287The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established.Keywords: Asymptotic stability; Constraint theory; Control system analysis; Control system synthesis; Costs; Linear control systems; Optimal control systems; Problem solving; Quadratic programming; Riccati equations; Constrained matrix differential Riccati equation Asymptotic analysis; Generalized Riccati equation; Indefinite stochastic linear quadratic (LQ) control; Linear matrix inequality; Solvability200110.1109/9.9114192015-12-10