Controllability of Delayed Discret Fornasini-Marchesini Model via Quantization and Random Packet Dropouts

¹ Department of Advanced Sciences and Technologies at National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Carthage, Tunisia
² Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Carthage, Tunisia

^* Corresponding author: adnen.arbi@gmail.com

Received: 22 May 2022
Accepted: 14 August 2022

Abstract

This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. The model takes into account the random packet loss and quantization errors in the network environment. So our modelling method has the potential to achieve a better stabilization effects. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.