Effects of noise variance model on optimal feedback design and actuator placement

In optimal placement of actuators for stochastic systems, it is commonly assumed that the actuator noise variances are not related to the feedback matrix and the actuator locations. In this paper, we will discuss the limitation of that assumption and develop a more practical noise variance model. Various properties associated with optimal actuator placement under the assumption of this noise variance model are discovered through the analytical study of a second order system.