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Decoupling transformation of singularly perturbed systems with small delays and its applications. (English) Zbl 0886.34063

Summary: For a 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 reduced-order approximate models, stability and stabilizability criteria. This transformation can be further used in different control problems.

MSC:

34K20 Stability theory of functional-differential equations
34K35 Control problems for functional-differential equations