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

: pp. 22–34
Received: September 11, 2020
Revised: November 24, 2020
Accepted: November 25, 2020
Laboratory of Analysis, Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University of Casablanca
Laboratory of Modelling, Analysis, Control and Statistics, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca
Laboratory of Analysis, modeling and simulation, Department of mathematics and computer sciences, Faculty of sciences Ben M'Sik, University Hassan II of Casablanca

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.

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Mathematical Modeling and Computing, Vol. 8, No. 1, pp. 22–34 (2021)