Measuring how far a controllable system is from an uncontrollable one
The main goal of this note is to explore some of the properties of a controllable system
which, in a precise sense to be defined, is near an uncontrollable pair. To do this, we first
discuss the notion of the distance between a controllable system and the nearest
uncontrollable one in both real and complex cases [2]-[5]. When this distance is relatively
small, we show to what extent this distance corresponds to certain properties of the
uncontrollability matrix and the reachability Grammian.
which, in a precise sense to be defined, is near an uncontrollable pair. To do this, we first
discuss the notion of the distance between a controllable system and the nearest
uncontrollable one in both real and complex cases [2]-[5]. When this distance is relatively
small, we show to what extent this distance corresponds to certain properties of the
uncontrollability matrix and the reachability Grammian.
The main goal of this note is to explore some of the properties of a controllable system which, in a precise sense to be defined, is near an uncontrollable pair. To do this, we first discuss the notion of the distance between a controllable system and the nearest uncontrollable one in both real and complex cases [2]-[5]. When this distance is relatively small, we show to what extent this distance corresponds to certain properties of the uncontrollability matrix and the reachability Grammian.
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