Boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures. (English) Zbl 1122.93067
Summary: We consider the problem of boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures that are governed by unstable linear reaction-convection-diffusion equations. We extend boundary feedback control laws designed for the one-dimensional reaction-diffusion equation using the backstepping method to this higher-dimensional case. We show that, under certain mathematical conditions on the velocity field, boundary feedback controls similar to the ones for one-dimensional equations also works for the higher dimensional case and exponentially stabilize the homogeneous equilibrium zero at any given decay rate.
MSC:
| 93D10 | Popov-type stability of feedback systems |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93C05 | Linear systems in control theory |
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