H2 norm of linear time-periodic systems: A perturbation analysis

Mihailo R. Jovanović

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


We consider a class of linear time-periodic systems in which dynamical generator A(t) represents a sum of a stable time-invariant operator A 0 and a small amplitude zero-mean T-periodic operator εA p(t). We employ a perturbation analysis to develop a computationally efficient method for determination of the H2 norm. Up to a second order in perturbation parameter SL we show that: a) the H2 norm can be obtained from a conveniently coupled system of readily solvable Lyapunov and Sylvester equations; b) there is no coupling between different harmonics of Ap(t) in the expression for the H2 norm. These two properties do not hold for arbitrary values of , and their derivation would not be possible if we tried to determine the H2 norm directly without resorting to perturbation analysis. Our method is well suited for identification of the values of period T that lead to the largest increase/reduction of the H2 norm. Two examples are provided to motivate the developments and illustrate the procedure.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424402107, 9781424402106
StatePublished - Jan 1 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2006 American Control Conference
Country/TerritoryUnited States
CityMinneapolis, MN


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