Lethargy results in lti system modelling

摘要

Modelling of lienar time-invariant (LTI) systems is studied in an approximate modelling framework notivated by modern robust control theory. The modelling results derived in this paper are mostly of lethargy type, i.e. they establish limitations in approximate modelling of LTI systems. Non-existence of copriime factorizations is established for a number of different types of LTI systems. This leads to the somewhat surprising conclusion that may LTI systems are not even stabilizable and that an even larger class of LTI systems can not be well-approximated by rational transfer function models. Furthermore, different definitions of the important finite power signal setup are studied and new results given.