Displaying similar documents to “Dynamic stabilization of systems via decoupling techniques”

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

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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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.

How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

George Weiss, Marius Tucsnak (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Let A 0 be a possibly unbounded positive operator on the Hilbert space H , which is boundedly invertible. Let C 0 be a bounded operator from 𝒟 A 0 1 2 to another Hilbert space U . We prove that the system of equations z ¨ ( t ) + A 0 z ( t ) + 1 2 C 0 * C 0 z ˙ ( t ) = C 0 * u ( t ) y ( t ) = - C 0 z ˙ ( t ) + u ( t ) , determines a well-posed linear system with input u and output y . The state of this system is x ( t ) = z ( t ) z ˙ ( t ) ∈ 𝒟 A 0 1 2 × H = X , where X is the state space. Moreover, we have the energy identity ∥ x ( t ) ∥ X 2 - ∥ x ( 0 ) ∥ X 2 = ∫ 0 T ∥ u ( t ) ∥ U 2 d t - ∫ 0 T ∥ y ( t ) ∥ U 2 d t . We show that the system described...

The stability of an irrigation canal system

Hamid Bounit (2003)

International Journal of Applied Mathematics and Computer Science

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In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the...