## The reachable set of a linear endogenous switching system

### Claudio Altafini

*Systems and Control Letters*, 47(4):343-353, 2002

In this work, switching systems are named endogenous when their switching pattern is controllable.
Linear endogenous switching systems can be considered as a particular class of driftless bilinear co
ntrol systems.
The key idea is that both types of systems are equivalent to
polysystems i.e. to systems whose flow is piecewise smooth.
The reachable set of a linear endogenous switching system can be studied consequently.
The main result is that, in general, it has the structure of a semigroup, even when the Lie algebra
rank condition is satisfied.

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