LAUSR

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 ℋ2 norm and the dual Lyapunov matrix of periodic systems with delays. We show that the primal and dual system have the same ℋ2 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.