# American Institute of Mathematical Sciences

January  1995, 1(1): 17-33. doi: 10.3934/dcds.1995.1.17

## Controllability of systems of interconnected membranes

 1 Department of Mathematics, Georgetown Univesity, Washington, DC 20057, United States

Received  September 1994 Published  December 1994

The problems of approximate, and exact, controllability of the transient behavior of a system of interconnected, two-dimensional elastic membranes in three dimensional space are considered. The membranes may have differing material properties. Control inputs and outputs are assumed to be restricted to the outer edges of the network and to the junction regions where two or more membranes are joined. The object is to characterize those membrane configurations which are approximately, or exactly, controllable. A class of membrane configurations which may be approximately controlled from the outer edges alone is identified. In particular, any two-membrane network may be approximately controlled from an arbitrarily small open subset of the outer boundary of one of the membranes. It is further proved that under some restrictions on the geometries of the individual membranes and the overall configuration, exactly controllability may be achieved through the action of controls along both the outer boundaries and in the junction regions of the network.
Citation: John E. Lagnese. Controllability of systems of interconnected membranes. Discrete & Continuous Dynamical Systems, 1995, 1 (1) : 17-33. doi: 10.3934/dcds.1995.1.17
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