IPACS Electronic library

SWITCHED LINEAR SYSTEMS. GEOMETRIC APPROACH

Dolors Magret, M. Eulalia Montoro
Switched linear systems constitute a class of nonlinear
systems whose behaviour has been subject of
study by researchers in recent years because of the
great number of areas from which they arise and their
interesting properties.
We consider a natural equivalence in the space of matrices
defining switched linear systems, which includes basis changes
in the state variables, inputs and outputs spaces, state
feedback and output injection, and in the case where
the subsystems are singular, also derivative feedback.
Equivalence classes coincide with the orbits under a
suitable Lie group action on the differentiable manifold
of matrices defining the systems. From this identification,
we can make a geometrical study: the dimension of equivalence classes are
deduced and miniversal deformations are obtained, following
Arnold’s techniques.
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