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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.

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
Full Text:
DOI

### References:

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