Exact Mixed Controllability

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 ).