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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 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....

Stabilization of wave systems with input delay in the boundary control

Gen Qi Xu, Siu Pang Yung, Leong Kwan Li (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight ( 1 - μ ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hilbert...

Static output feedback controller design

Vojtech Veselý (2001)

Kybernetika

In this paper new necessary and sufficient conditions for static output feedback stabilizability for continuous and discrete time linear time invariant systems have been proposed. These conditions form the basis for the procedure of static output feedback controller design proposed in this paper. The proposed LMI based algorithms are computationally simple and tightly connected with the Lyapunov stability theory and LQ optimal state feedback design. The structure of the output feedback gain matrix,...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...

Structurally stable design of output regulation for a class of nonlinear systems

Celia Villanueva-Novelo, Sergej Čelikovský, Bernardino Castillo-Toledo (2001)

Kybernetika

The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem...

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