Covariance Control of Linear Discrete-time Stochastic Systems

The idea of covariance control is to construct the state covariance matrix (P) according to the desired performance of the linear stochastic system and then to assign this P to the closed-loop stochastic system. Our approach deals with the problem of describing a covariance state space model for stochastic systems. We employ a control design methodology based on integral control approach which guarantees state covariance stability. The covariance of any state variable is also guaranteed to track a predetermined value precisely. This paper tends to define covariance tracking error as a new state of the covariance system and with this augmented state, the state covariance feedback controller K could be determined, to achieve both state covariance stability and state covariance tracking for linear discrete-time stochastic systems.