Asymptotic approximations validity boundaries for decoupling transformation of three-time-scale linear time-invariant singularly perturbed systems with delay
Abstract:
For time-invariant singularly perturbed control systems with state delay the method of separation of movements is
evolved on the basis of Chang-type non-degenerate transformation. Asymptotic approximations for completely separated
subsystems of the considered singularly perturbed system with three-time scales are introduced, boundaries of values of small
singularity parameters are constructed and proved, which guarantee the validity of asymptotic representations and estimates of
solutions underlying matrix operator equations, asymptotic approximations for the decoupling transformation and matrix
operators of the split system. An illustrative example is given.
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