This monograph provides a rigorous treatment of problems related to partial asymptotic
stability and controllability for models of flexible structures described by coupled nonlinear
ordinary and partial differential equations or equations in abstract spaces. The text is
self-contained beginning with some basic results from the theory of continuous semigroups of
operators in Banach spaces. The problem of partial asymptotic stability with respect to a
continuous functional is then considered for a class of abstract multivalued systems on a
metric space. Next the results of this study are applied to the study of a rotating body with
elastic attachments. Professor Zuyev demonstrates that the equilibrium cannot be made strongly
asymptotically stable in the general case motivating consideration of the problem of partial
stabilization with respect to the functional that represents averaged oscillations. The book's
focus moves on to spillover analysis for infinite-dimensional systems with finite-dimensional
controls. It is shown that a family of L2-minimal controls corresponding to low frequencies
can be used to obtain approximate solutions of the steering problem for the complete system.
The book turns from the examination of an abstract class of systems to particular physical
examples. Timoshenko beam theory is exploited in studying a mathematical model of a
flexible-link manipulator. Finally a mechanical system consisting of a rigid body with the
Kirchhoff plate is considered. Having established that such a system is not controllable in
general sufficient controllability conditions are proposed for the dynamics on an invariant
manifold. Academic researchers and graduate students interested in control theory and
mechanical engineering will find Partial Stabilization and Control of Distributed-Parameter
Systems with Elastic Elements a valuable and authoritative resource for investigations on the
subject of partial stabilization.
