On the Theory of State-Covariance Assignment for Single-Input Linear Discrete Systems

In this paper, alternative method for state-covariance assignment for single-input linear systems is proposed. New formulas for linear discrete systems are presented. These formulas are based on the inverse solutions of Lyapunov equations and are similar to the formulas for pole placement. The set of all assignable covariance matrices to a single-input discrete system is also characterized.