Controllability conditions of linear singularly perturbed systems with small state and input delays. (English) Zbl 1338.93075
Summary: A singularly perturbed linear time-dependent controlled system with a point-wise delay in state and control variables is considered. The delay is small of order of the small positive multiplier for a part of the derivatives in the system, which is a parameter of the singular perturbation. Two types of the original singularly perturbed system, standard and nonstandard, are analyzed. For each type, two much simpler parameter-free subsystems (the slow and fast ones) are associated with the original system. It is established in the paper that proper kinds of controllability of the slow and fast subsystems yield the complete Euclidean space controllability of the original system robustly with respect to the parameter of singular perturbation for all its sufficiently small values. Illustrative examples are presented.
MSC:
| 93B05 | Controllability |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
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