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Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs. (English) Zbl 1350.93032
Summary: 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
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