On the asymptotic output sensitivity problem for a discrete linear systems with an uncertain initial state

Abstract

This paper studies a finite-dimensional discrete linear system whose initial state $x_0$ is unknown. We assume that the system is augmented by two output equations, the first one $z_i$ being representing measurements made on the unknown state of the system and the other $y_i$ being representing the corresponding output. The purpose of our work is to introduce two control laws, both in closed-loop of measurements $z_i$ and whose goal is to reduce asymptotically the effects of the unknown part of the initial state $x_0$. The approach that we present consists of both theoretical and algorithmic characterization of the set of such controls. To illustrate our theoretical results, we give a number of examples and numerical simulations.