  This paper presents a four-stage algorithm for the realization of
multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov
parameters. In the first stage, a linear time-varying (LTV) realization that is
topologically equivalent to the true SLS is derived from the Markov parameters
assuming that the submodels have a common MacMillan degree and a mild condition
on their dwell times holds. In the second stage, zero sets of LTV Hankel
matrices where the realized system has a linear time-invariant (LTI) pulse
response matching that of the original SLS are exploited to extract the
submodels, up to arbitrary similarity transformations, by a clustering
algorithm using a statistics that is invariant to similarity transformations.
Recovery is shown to be complete if the dwell times are sufficiently long and
some mild identifiability conditions are met. In the third stage, the switching
sequence is estimated by three schemes. The first scheme is based on
forward/backward corrections and works on the short segments. The second scheme
matches Markov parameter estimates to the true parameters for LTV systems and
works on the medium-to-long segments. The third scheme also matches Markov
parameters, but for LTI systems only and works on the very short segments. In
the fourth stage, the submodels estimated in Stage 2 are brought to a common
basis by applying a novel basis transformation method which is necessary before
performing output predictions to given inputs. A numerical example illustrates
the properties of the realization algorithm. A key role in this algorithm is
played by time-dependent switching sequences that partition the state-space
according to time, unlike many other works in the literature in which
partitioning is state and/or input dependent.
