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Open AccessArticle

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

Faculty of Economics and Management, Yanka Kupala State University of Grodno, 230023 Grodno, Belarus
Axioms 2019, 8(2), 71; https://doi.org/10.3390/axioms8020071
Received: 19 February 2019 / Revised: 26 April 2019 / Accepted: 23 May 2019 / Published: 3 June 2019
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 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 and the boundary layer system. View Full-Text
Keywords: time delay system; multiple commensurate delays; singular perturbation; decomposition; Chang transformation; complete controllability; robust sufficient condition time delay system; multiple commensurate delays; singular perturbation; decomposition; Chang transformation; complete controllability; robust sufficient condition
MDPI and ACS Style

Tsekhan, O. Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation. Axioms 2019, 8, 71.

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