Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs.

*(English)*Zbl 1350.93032Summary: Necessary and sufficiently conditions are derived for the decomposition of a second order linear time-varying system into two cascade connected commutative first order linear time-varying subsystems. Explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.

##### MSC:

93B17 | Transformations |

93B11 | System structure simplification |

93A30 | Mathematical modelling of systems (MSC2010) |

93B35 | Sensitivity (robustness) |

93C05 | Linear systems in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

93C99 | Model systems in control theory |

34A30 | Linear ordinary differential equations and systems |

34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |

##### Keywords:

differential equations; analogue control; equivalent circuits; feedback circuits; feedback control systems; robust control
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##### References:

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