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

Zuyev, Alexander

Automatica 41, No. 1, 1-10 (2005).

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.

Reviewer: Stefan Zanfir (Craiova)

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

Keywords:

stabilization; nonlinear control; partial stability; Lyapunov function; infinite-dimensional systems; coupled rigid and elastic parts; hybrid system; rigid body; elastic beams

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