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• W3014493752 abstract "Summary We present novel theoretical concepts for linear time‐periodic systems with multiple delays, which are closely related to the spectral properties and Lyapunov matrices. At the basis of the main results is the associated dual system, constructed by transposition of the systems matrices and affine transformations of their arguments. We introduce, for the first time, the concepts of the norm and the dual Lyapunov matrix of periodic systems with delays. We show that the primal and dual system have the same norm, characterized by primal and dual delay Lyapunov equations, which extend the well‐known results for time‐invariant systems with delays, and periodic systems without delays. Having at hand the pair of primal‐dual Lyapunov matrices, along with some energy interpretations, allow us to generalize the concept of position balancing and explore its potential for model reduction. The obtained results are illustrated by several examples, including the delayed Mathieu equation." @default.
• W3014493752 created "2020-04-10" @default.
• W3014493752 creator A5008378186 @default.
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• W3014493752 date "2020-04-01" @default.
• W3014493752 modified "2023-09-25" @default.
• W3014493752 title "On the dual linear periodic time‐delay system: Spectrum and Lyapunov matrices, with application to analysis and balancing" @default.
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• W3014493752 doi "https://doi.org/10.1002/rnc.4970" @default.
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