Approximation of State-Affine Discrete-Time Systems using Q-Volterra Covariance Equivalent Realizations

A method is presented for constructing lower order approximations of state-affine discrete-time systems which match exactly a specified number of two types of system parameters: a set of Volterra parameters relating to the transient response and a set of covariance parameters relating to the steady state stochastic response. The infinite sets of these parameters provide fundamental descriptions for the input-output map and the input-output correlations of the system. An algorithm is developed that leads to a set of reduced order models which match exactly a finite number of Volterra and covariance parameters. Examples are given to demonstrate the attributes of the method.