Stabilization of Elastic Systems by Collocated Feedback

1. Front Matter

   Pages i-xi

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2. Some Backgrounds

   • Kaïs Ammari, Serge Nicaise

   Pages 1-35

3. Stabilization of Second Order Evolution Equations by a Class of Unbounded Feedbacks

   • Kaïs Ammari, Serge Nicaise

   Pages 37-60

4. Stabilization of Second Order Evolution Equations with Unbounded Feedback with Delay

   • Kaïs Ammari, Serge Nicaise

   Pages 61-71

5. Asymptotic Behaviour of Concrete Dissipative Systems

   • Kaïs Ammari, Serge Nicaise

   Pages 73-146

6. Systems with Delay

   • Kaïs Ammari, Serge Nicaise

   Pages 147-168

7. Back Matter

   Pages 169-180

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By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.

• 93D15,93B07,93B05,93B52,93C15,93C20,35L05,35L57,35Q74,35M33.
• Collocated feedbacks
• Elastic systems
• Observability
• PDE
• Stability
• partial differential equations

• Dept of Mathematics, Faculty of Sciences, University of Monastir, Monastir, Tunisia

  Kaïs Ammari

• Lab. de Mathématiques et de leurs applications de Valenciennes (LAMAV), Univ. de Valenciennes et du Hainaut Cambrésis, Valenciennes, France

  Serge Nicaise

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