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Vibrational stabilizability of distributed parameter systems. (English) Zbl 0554.93059
Stabilizability of linear distributed parameter systems by introduction of zero mean oscillations in the system coefficients is analysed. By means of a finite dimensional approximation a condition for vibrational stabilizability of a second order (with respect to time) partial differential equation is given. As an example of vibrational stabilization of nonlinear systems the stabilization condition for the hydrodynamic equations of the Bénard problem is derived.
Reviewer: A.Tylikowski

MSC:
93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
35B35 Stability in context of PDEs
76E30 Nonlinear effects in hydrodynamic stability
70J25 Stability for problems in linear vibration theory
70K20 Stability for nonlinear problems in mechanics
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