  Switched systems are capable of modeling processes with underlying dynamics
that may change abruptly over time. To achieve accurate modeling in practice,
one may need a large number of modes, but this may in turn increase the model
complexity drastically. Existing work on reducing system complexity mainly
considers state space reduction, yet reducing the number of modes is less
studied. In this work, we consider Markov jump linear systems (MJSs), a special
class of switched systems where the active mode switches according to a Markov
chain, and several issues associated with its mode complexity. Specifically,
inspired by clustering techniques from unsupervised learning, we are able to
construct a reduced MJS with fewer modes that approximates well the original
MJS under various metrics. Furthermore, both theoretically and empirically, we
show how one can use the reduced MJS to analyze stability and design
controllers with significant reduction in computational cost while achieving
guaranteed accuracy.
