Geodesic
Controllability of evolution equations and inclusions driven by vector measures
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 24 (2004) no. 1, pp. 49-72.

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In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
Keywords: controlability, impulsive systems, differential inclusions, Hilbert spaces, vector valued measures, C₀ semigroups 
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Ahmed, N.U. Controllability of evolution equations and inclusions driven by vector measures. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 24 (2004) no. 1, pp. 49-72. http://geodesic.mathdoc.fr/item/DMDICO_2004_24_1_a4/

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