First and second moment control of linear stochastic discrete time systems

This paper deals with control of first and second moment of the states of linear stochastic discrete-time systems. In this paper, the expectation and covariance of the states are combined together to construct a new higher order system. Our approach tends to use the covariance and the expectation of the states as feedback signals to obtain the appropriate control signal which leads the states of the open loop system to a prescribed value for expectation vector and covariance matrix. The resulted system is deterministic, so we would be able to choose any well-defined control design method. In this paper, the method is based on integral control approach. The expectation and covariance of any state of the system are guaranteed to track the desired corresponding values.