Stabilization of Elastic Systems by Collocated Feedback

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.

Inhalt

Some backgrounds.- Stabilization of second order evolution equations by a class of unbounded feedbacks.- Stabilization of second order evolution equations with unbounded feedback with delay.- Asymptotic behaviour of concrete dissipative systems.- Systems with delay.- Bibliography