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The real story behind Floquet-Lyapunov theory


Floquet-Lyapunov theory plays a ubiquitous role in the analysis and control of time-periodic systems. A real linear system with T-periodic coefficients will generally lead to a complex Floquet factorization. However, it is well known that by regarding the system as having 2T-periodic coefficients, it is possible to obtain real factors. In this paper, we show that there exists a simple way to define real factors using known results for the real matrix logarithm and the knowledge of the state transition matrix of the system on a single period. The proposed procedure also determines whether the real Lyapunov transformation is T-periodic, T-antiperiodic, or generally 2T-periodic.

Authors: Raymond J. Spiteri, Pierre Montagnier

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