1. Spectrum rearrangement via feedback control for nonhomogeneous damped string.
- Author
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Shubov, Marianna A.
- Subjects
- *
EIGENVALUES , *EIGENFUNCTIONS , *NUMERICAL solutions to boundary value problems , *NUMERICAL solutions to differential equations , *NUMERICAL solutions to integral equations , *HILBERT space - Abstract
The solution of the pole reassignment control problem for a distributed parameter system is presented. The system is a vibrating string with spatially non-homogeneous density and modulus of elasticity coefficients and with both distributed and boundary damping. The string equation and the boundary conditions are reduced to a single linear evolution equation in the Hilbert space of two-component Cauchy data equipped with energy metric. It is the dynamics generator of this equation, whose spectrum is rearranged with a feedback control. The solution is based on the fact that the dynamics generator, its finite-rank perturbations and the adjoints to these operators are Riesz spectral, i.e. their sets of the generalized eigenvectors form (non-orthogonal) Riesz bases in the state space. The approach extends to any system, whose dynamics generator has similar properties. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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