Deviations estimates for uncertain time-varying discrete-time systems

The paper develops a mathematical framework within which an analysis of finite horizon control problems for uncertain non-stationary linear discrete-time systems. Uncertainty in the system description is modelled by an unknown (norm bounded) additive perturbation of the system matrix. It is assumed that the nominal control has feedback form and when applied to the nominal, unperturbed system produces nominal state and output. If we now apply this control to uncertain system the state and output will be (in general) different. In this paper we derive estimates for the deviations of the output of perturbed system from the output of the nominal (unperturbed) one. These estimates use norms of certain dynamical. operators defined on a finite time interval. For computing of these operator norms we present a method based on parameterised difference Riccati equations. As example, estimating for control problem of communication satellite is presented. Copyright (C) 2000 IFAC.