The homological perturbation lemma and its applications to robust stabilization

Abstract : Within the lattice approach to analysis and synthesis problems, we show how standard results on robust stabilization can be obtained in a unified way and generalized when interpreted as a particular case of the so-called homological perturbation lemma. This lemma plays a significant role in algebraic topology, homological algebra, computer algebra, etc. Our results show that it is also central to robust control theory for (infinite-dimensional) linear systems.