Approximation of Limit Cycles by Using Planar Switching Affine Systems with Guarantees for Uniqueness and Stability

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This paper proposes a novel method to approximate a stable and unique limit cycle, as obtained e.g. from simulation of a nonlinear model or from experimental data, by a planar switching affine system (PSAS) while preserving the properties of uniqueness and stability. In contrast to existing literature, which formulates elaborate procedures based on system transformation to conclude on stability and uniqueness, this paper provides easy to check sufficient conditions directly formulated for the PSAS. Those conditions then serve as equality and inequality constraints in an optimization problem to determine the model parameters of the PSAS which best approximate the data points measured for the given limit cycle. It is shown that the sufficient conditions lead to the same results as formulated in literature, while a system transformation is not necessary. Efficiency, flexibility, and performance of the proposed method are demonstrated for a numeric example.

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