Abstract
We investigate some stability properties of approximate null-controllability (A0C). We show that A0C is inherited when increasing the number of observed jumps. However, in all generality, there is no direct connection between A0C with an initial mode and the A0C starting from directly accessible modes. We have also given a sufficient condition under which checking A0C implies AC and discuss some examples. Unfortunately, such conditions are too strong and do not cover all AC systems (see examples). In a second part, we give a Riccati technique-based viability kernel characterisation of A0C. Some conditions are inferred for AC.
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