Exact Covariance Characterization for Controlled Linear Systems subject to Stochastic Parametric and Additive Uncertainties

This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization, the problem of control design for state covariance dynamics is addressed, providing conditions that are conservative yet more tractable compared to standard necessary and sufficient ones for the same class of systems. Numerical results assess this new characterization by comparing it to the empirical covariance and illustrate the control design problem.