Feedback Stabilization of some Second Order Systems

The aim of this book is to present some recent results on the stabilization of some second order linear systems. In particular, emphasis is placed on two types of output feedback stabilization. In the first axis, we are interested in the static output feedback stabilization. Precisely, we showed that the exponential stability of a second order equation with delay is reduced to the observability inequality of the conservative associated one. Analogous results are being established for a coupled second order system without and with delay when the control and coupling operators are unbounded. The second axis is devoted to study the dynamic feedback stabilization. Namely, we are interested in a system coupling second order equation (Hyperbolic) with a first order equation (Parabolic) known as a thermoelastic system. Using decoupling technique we showed the compactness of the difference between the semigroups generated by the thermoelastic system and its decoupled one. We established the same results for thermoviscoelastic system. This book represents a useful reference for graduate students, physicists, theoretical engineers and researchers dealing with similar research topics.