Abstract
Under a suitable balanced distribution of observations, system \((I\!\!I^*)\) can be decomposed into two subsystems which will be separately observed by boundary and internal observations, respectively. Then the condition \({{\,\textrm{rank}\,}}(D)= N\) with \(D=(D_1,D_2)\) is indeed sufficient for the exact controllability of system \((I\!\!I)\) by mixed controls (H, G) under the multiplier control condition (3.2.6).
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References
Li, T.-T., Rao, B.-P.: Exact controllability and synchronization for a coupled system of wave equations with mixed internal and boundary controls, to appear
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Li, T., Rao, B. (2024). Exact Mixed Controllability. In: Synchronization for Wave Equations with Locally Distributed Controls. Series in Contemporary Mathematics, vol 5. Springer, Singapore. https://doi.org/10.1007/978-981-97-0992-2_15
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DOI: https://doi.org/10.1007/978-981-97-0992-2_15
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