This paper tackles the basis selection issue in the context of state-space
hybrid system identification from input-output data. It is often the case that
an identification scheme responsible for state-space switched linear system
(SLS) estimation from input-output data operates on local levels. Such
individually identified local estimates reside in distinct state bases, which
call for the need to perform some basis correction mechanism that facilitates
their coherent patching for the ultimate goal of performing output predictions
for predefined input test signals. We derive necessary and sufficient
conditions on the submodel set, the switching sequence, and the dwell times
that guarantee the presented approach's success. Such conditions turn out to be
relatively mild, which contributes to the application potential of the devised
algorithm. We also provide a linkage between this work and the existing
literature by providing several insightful remarks that highlight the discussed
method's favorability. We supplement the theoretical findings by an elaborative
numerical simulation that puts our methodology into action