Model Reduction of Discrete-Time Linear Systems with White Noise Coefficients

摘要

In this paper we investigate the model reduction problem of a class of discrete-time, linear, parameter-varying systems, where the parameter space is a finite set. Our complexity measure is the dimension of the state space realization of the system. In order to define distance metrics that can be used to compare two models with each other, we consider the case where the underlying parameter enters the system equations in a stochastic fashion and we introduce accordingly expected L2 gain based error measures. The main point of our reduction method is the formulation of two generalized dissipation inequalities that in conjuction with a suitably defined storage function enable us to derive reduced order models that come with a provable apriori upper bound on the approximation error.