Displaying similar documents to “Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control”

Low-Dimensional Description of Pulses under the Action of Global Feedback Control

Y. Kanevsky, A. A. Nepomnyashchy (2012)

Mathematical Modelling of Natural Phenomena

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The influence of a global delayed feedback control which acts on a system governed by a subcritical complex Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the framework of those models, one-pulse and two-pulse solutions are found, and their linear stability analysis is carried out. The application of the finite-dimensional model ...

The control of drilling vibrations: A coupled PDE-ODE modeling approach

Belem Saldivar, Sabine Mondié, Juan Carlos Avila Vilchis (2016)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE) through a nonlinear function describing the rock-bit interaction. We propose a systematic method to design feedback controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of harmful dynamics....

A multi-model approach to Saint-Venant equations: A stability study by LMIs

Valérie Dos Santos Martins, Mickael Rodrigues, Mamadou Diagne (2012)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear...

Robust exponential stability of a class of nonlinear systems

Vojtech Veselý, Danica Rosinová (1998)

Kybernetika

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The paper addresses the problem of design of a robust controller for a class of nonlinear uncertain systems to guarantee the prescribed decay rate of exponential stability. The bounded deterministic uncertainties are considered both in a studied system and its input part. The proposed approach does not employ matching conditions.