Basis transform in switched linear system state-space models from input-output data

This paper addresses the problem of basis correction in the context of LSS identification from input-output data. It is often the case that identification algorithms for the LSSs from input-output data operate locally. The individually identified local submodel estimates reside in distinct state bases, which mandates performing a basis correction that facilitates their coherent patching for the ultimate goal of performing output predictions for arbitrary inputs and switching sequences. We formulate a persistence of excitation condition for the inputs and the switching sequences that guarantee the presented approach's success. These conditions are mild in nature, which proves the practicality of the devised algorithm. We supplement the theoretical findings with an elaborating numerical simulation example.