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This paper addresses the mean-square optimal control problem for \a class ofdiscrete-time linear systems with a quasi-colored control-dependentmultiplicative noise via output feedback. The noise under study is novel andshown to have advantage on modeling a class of network phenomena such as randomtransmission delays. The optimal output feedback controller is designed usingan optimal mean-square state feedback gain and two observer gains, which aredetermined by the mean-square stabilizing solution to a modified algebraicRiccati equation (MARE), provided that the plant is minimum-phase andleft-invertible. A necessary and sufficient condition for the existence of thestabilizing solution to the MARE is explicitly presented. It shows that theseparation principle holds in a certain sense for the optimal control design ofthe work. The result is also applied to the optimal control problems innetworked systems with random transmission delays and analog erasure channels,respectively.

Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise