Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

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The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered.An approach to the time-scale separation of the original opi tenacious spirit singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used.Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained.

The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values.The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system roman atwood gfuel and the boundary layer system.