Abstract
A singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two lower-dimension systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. The reduced-order and the boundary-layer systems are in separate time scales, and they do not contain the small parameter any more. Connections between the properties of controllability of these systems and such a property of the original system itself are established for all sufficiently small values of the parameter of singular perturbations.
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Glizer, V.Y. Controllability of Singularly Perturbed Linear Time-Dependent Systems with Small State Delay. Dynamics and Control 11, 261–281 (2001). https://doi.org/10.1023/A:1015276121625
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DOI: https://doi.org/10.1023/A:1015276121625