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Stability result for a thermoelastic Bresse system with delay term in the internal feedback

Lamine Bouzettouta, Sabah Baibeche, Manel Abdelli, Amar Guesmia (2023)

Mathematica Bohemica

The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first considered...

Stabilizability and controllability of systems associated to linear skew-product semiflows.

Mihail Megan, Adina Luminita Sasu, Bogdan Sasu (2002)

Revista Matemática Complutense

This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....

Stabilization of a 1-D tank modeled by the shallow water equations

Christophe Prieur, Jonathan de Halleux (2002)

Journées équations aux dérivées partielles

We consider a tank containing a fluid. The tank is subjected to a one-dimensional horizontal move and the motion of the fluid is described by the shallow water equations. By means of a Lyapunov approach, we deduce control laws to stabilize the fluid's state and the tank's position. Although global asymptotic stability is yet to be proved, we numerically simulate the system and observe the stabilization for different control situations.

Stabilization of a coupled multidimensional system.

Serge Nicaise, Abdoulaye Sène (2006)

Revista Matemática Complutense

We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.

Stabilization of a hybrid system with a nonlinear nonmonotone feedback

Eduard FEIREISL, Geoffrey O'DOWD (2010)

ESAIM: Control, Optimisation and Calculus of Variations

For a hybrid system composed of a cable with masses at both ends, we prove the existence of solutions for a class of nonlinear and nonmonotone feedback laws by means of a priori estimates. Assuming some local monotonicity, strong stabilization is obtained thanks to some Riemann's invariants technique and La Salle's principle.

Stabilization of a layered piezoelectric 3-D body by boundary dissipation

Boris Kapitonov, Bernadette Miara, Gustavo Perla Menzala (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...

Stabilization of fractional exponential systems including delays

Catherine Bonnet, Jonathan R. Partington (2001)

Kybernetika

This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular...

Stabilization of homogeneous polynomial systems in the plane

Hamadi Jerbi, Thouraya Kharrat, Khaled Sioud (2016)

Kybernetika

In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on ℝ 2 ∖ { ( 0 , 0 ) } and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.

Currently displaying 41 – 60 of 79