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Partial asymptotic stabilization of nonlinear distributed parameter systems. (English) Zbl 1067.93037

The paper develops the problems of modelling and control for mechanical systems consisting of coupled absolutely rigid and elastic parts. First, the author considers the abstract Cauchy problem in a Banach space and proves the basic results on partial asymptotic stability. Then he establishes a mathematical model of a hybrid system consisting of a rigid body and several elastic beams. Within the framework of the Lagrangian formalism, he obtains the equations of motion for such an infinite-dimensional system. To this model he applies the above results, develops a stabilizing feedback law, and establishes sufficient conditions for asymptotic stability and stabilizability. Finally, some simulation results are presented.

MSC:

93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H55 Stability of dynamical problems in solid mechanics
70E55 Dynamics of multibody systems
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