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Frequency Criterion of Robust Modality for the Class of Linear Systems with Time-delays

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  • Control Theory and Applications
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Abstract

A class of linear systems described by rational transfer functions with interval parameters and fixed time-delay values is considered in this study. The ranges of variation of the interval parameters depends on the total range of perturbations. A sufficient frequency criterion for robust modality is formulated. This criterion is determined by the inclusion of all the roots of a system characteristic quasi-polynomial to the region located to the left of the given position of the vertical boundary. The advantage of the developed criterion in comparison with similar ones is the possibility of refusing to analyze the set of characteristic quasi-polynomials of the system, as well as refusing to analyze the nominal system. This provides by constructioning and studying only two hodographs. In special cases, the developed criterion coincides with the known frequency criteria for system analysis.

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Authors and Affiliations

  1. Department of Technical Cybernetics, Belgorod State Technological University named after V.G. Shukhov, 46 Kostyukova St., Belgorod, 308012, Russian Federation

    Ilya Aleksandrovich Rybin & Vasiliy Grigorievich Rubanov

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  1. Ilya Aleksandrovich Rybin
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  2. Vasiliy Grigorievich Rubanov
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Correspondence to Ilya Aleksandrovich Rybin.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Nam H. Jo under the direction of Editor PooGyeon Park. This work is supported by the Ministry of Science and Higher Education of the Russian Federation within the Public contract project 2.1396.2017/4.6.

Ilya Aleksandrovich Rybin received his M.S. degree in computer science and engineering, and Candidate of Engineering Sciences degree from Belgorod State Technological University n.a. V.G. Shukhov, in 2014 and 2019, respectively. He is currently an Associate Professor at the Department of Technical Cybernetics, Belgorod State Technological University n.a. V.G. Shukhov, Russia. His research interests include methods of analysis and synthesis of automatic control systems.

Vasiliy Grigorievich Rubanov received the Specialist degree in aircraft control systems, and a Doctor of Engineering Sciences degree from Belgorod Technological Institute of Building Materials, in 1965 and 1992, respectively. He is currently a Head of the Department of Technical Cybernetics, Belgorod State Technological University n.a. V.G. Shukhov, Russia. His research interests include automatic control theory and robust control.

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Rybin, I.A., Rubanov, V.G. Frequency Criterion of Robust Modality for the Class of Linear Systems with Time-delays. Int. J. Control Autom. Syst. 19, 745–752 (2021). https://doi.org/10.1007/s12555-019-0562-y

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  • DOI: https://doi.org/10.1007/s12555-019-0562-y

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