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

Ilya Aleksandrovich Rybin* and Vasiliy Grigorievich Rubanov
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.745-752, 2021

Abstract : A class of linear systems described by rational transfer functions with interval parameters and fixed timedelay 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.

Keyword : Analysis criterion, interval parameters, robust modality, robust stability, system with time-delays.

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