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Decoupling Transformation of Singularly Perturbed Systems with Small Delays and Its Applications

机译:时滞奇摄动系统的解耦变换及其应用

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摘要

For linear singularly perturbed system of functional differential equations with small time delays we find a change of variables that decomposes this system into a purely-slow system of ordinary differential equations and a purely-fast functional equation. This decomposition is a generalization of Chang's decoupling transformation of singularly perturbed systems in the time-delay case. It is obtained by virtue of invariant manifolds and it can be found approximately in the form of asymptotic expansion. Using this transformation we get the reduced-order approximate models, stability and stabilizability criteria. This transformation can be further used in different control problems.
机译:对于具有较小时滞的线性奇摄动泛函微分方程组,我们发现变量的变化将其分解为纯慢速方程组和纯快速泛函方程组。这种分解是在时滞情况下Chang奇异摄动系统解耦变换的推广。它是通过不变流形获得的,并且可以近似地以渐近展开的形式找到。使用此变换,我们获得了降阶近似模型,稳定性和稳定性标准。该变换可以进一步用于不同的控制问题。

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