Explicit expressions for the H2 norm of time-delay systems based on the delay lyapunov equation
2010 (English)In: Proceedings of the 49th IEEE Conference on Decision and Control, 2010Conference paper (Refereed)
It is widely known that the solutions of Lyapunov equations can be used to compute the H2 norm of linear time-invariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. We establish, in the main result, that the H2 norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the relation with the delay Lyapunov equation we can prove an explicit formula for the H2 norm if the system has commensurate delays, here meaning that the delays are all integer multiples of a basic delay. The formula is explicit and contains only elementary linear algebra operations applied to matrices of finite dimension.
Place, publisher, year, edition, pages
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-53374DOI: 10.1109/CDC.2010.5717782ScopusID: 2-s2.0-79953132471OAI: oai:DiVA.org:kth-53374DiVA: diva2:470009
49th IEEE Conference on Decision and Control, Atlanta Georgia, USA 15-17 December 2010
QC 201202072011-12-272011-12-272012-02-07Bibliographically approved