Abstract
The paper introduces the study of in-block controllability (IBC) of controlled switched linear systems on polytopes, which formalizes controllability of controlled switched linear systems under state constraints. In particular, for a given switched linear system and a given polytope, representing the state constraints, we study whether all the states in the interior of the polytope are mutually accessible through its interior using proper switching functions and uniformly bounded control inputs. By studying the geometry of the problem, we provide three necessary conditions for IBC. Then, we provide two cases where these necessary conditions are also sufficient. We also give illustrative examples of the main results.
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