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

Adnène Arbi^1, 2

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

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 38.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2022040

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