Abstract
We introduce a general formalism for linear evolution equations with skew adjoint operators. We make explicit the controllability operator as an expansion with respect to eigenfunctions. Using the fact that the eigenvalues are purely imaginary, we give sufficient controllability conditions. This approach is convenient for studying the asymptotic behaviour of the optimal control.
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Bensoussan, A. On the general theory of exact controllability for skew symmetric operators. Acta Appl Math 20, 197–229 (1990). https://doi.org/10.1007/BF00049568
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DOI: https://doi.org/10.1007/BF00049568