 
Summary: The reachable set of a linear endogenous switching
system
Claudio Altafini
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy; altafini@sissa.it
August 6, 2002
Abstract
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 bilinear control 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 since the logic inputs cannot reverse the direction
of the flow. The adaptation of existing controllability criteria for bilinear systems is
straightforward.
Keywords: Linear switching systems, bilinear control systems, polysystems, reachability
semigroups, controllability.
1 Introduction
