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We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential… (More)

— This paper deals with the robust exact pole placement problem in connection with the solvability of a Sylvester equation. The main issue is to compute a well-conditioned solution to this equation. The best candidate solution must possess the minimal condition number. This problem is cast as a global optimization under LMI constraints for which a numerical… (More)

—The 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… (More)