Basis transform in linear switched system models from input–output data

Abstract

SummaryThis article addresses the problem of basis correction in the context of linear switched‐system (LSS) identification from input–output data. It is often the case that identification algorithms for the LSSs from input–output data operate locally. The local submodel estimates, identified individually by subspace algorithms from the input‐output data, reside in different‐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 guarantees 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.