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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.

Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback

Patrick Florchinger (2016)

Kybernetika

In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this...

Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback

Patrick Florchinger (2018)

Kybernetika

In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this...

Stabilization of nonlinear systems with varying parameter by a control Lyapunov function

Wajdi Kallel, Thouraya Kharrat (2017)

Kybernetika

In this paper, we provide an explicit homogeneous feedback control with the requirement that a control Lyapunov function exists for affine in control systems with bounded parameter that satisfies an homogeneous condition. We use a modified version of the Sontag's formula to achieve our main goal. Moreover, we prove that the existence of an homogeneous control Lyapunov function for an homogeneous system leads to an homogeneous closed-loop system which is asymptotically stable by an homogeneous feedback...

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Stabilization of second order evolution equations with unbounded feedback with delay

Serge Nicaise, Julie Valein (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider abstract second order evolution equations with unbounded feedback with delay. Existence results are obtained under some realistic assumptions. Sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability. Some new examples that enter into our abstract framework are presented.

Stabilization of second-order systems by non-linear feedback

Paweł Skruch (2004)

International Journal of Applied Mathematics and Computer Science

A stabilization problem of second-order systems by non-linear feedback is considered. We discuss the case when only position feedback is available. The non-linear stabilizer is constructed by placing actuators and sensors in the same location and by using a parallel compensator. The stability of the closed-loop system is proved by LaSalle's theorem. The distinctive feature of the solution is that no transformation to a first-order system is invoked. The results of analytic and numerical computations...

Stabilization of the wave equation by on-off and positive-negative feedbacks

Patrick Martinez, Judith Vancostenoble (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback a ( t ) u t . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a : typically a is equal to 1 on ( 0 , T ) , equal to 0 on ( T , q T ) and is q T -periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability. In both cases,...

Stabilization of the wave equation by on-off and positive-negative feedbacks

Patrick Martinez, Judith Vancostenoble (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback a ( t ) u t . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a: typically a is equal to 1 on (0,T), equal to 0 on (T, qT) and is qT-periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability....

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