# American Institute of Mathematical Sciences

## Minimum energy compensation for discrete delayed systems with disturbances

 Faculty of Sciences Ain Chock, University Hassan II, B.P.5366, Maȃrif, Casablanca, Morocco

* Corresponding author

Received  October 2018 Revised  January 2019 Published  October 2019

This work is devoted to the remediability problem for a class of discrete delayed systems. We investigate the possibility of reducing the disturbance effect with a convenient choice of the control operator. We give the main properties and characterization results of this concept, according to the delay and the observation. Then, under an appropriate hypothesis, we demonstrate how to find the optimal control which ensures the compensation of a disturbance measured through the observation (measurements, signals, ...). The discrete version of the wave equation, as well as the usual actuators and sensors, are examined. Numerical results are also presented.

Citation: Salma Souhaile, Larbi Afifi. Minimum energy compensation for discrete delayed systems with disturbances. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020119
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Control observation for $N = 10$
Control observation for $N = 20$