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Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers
Author(s) -
Ghorbani Majid,
TavakoliKakhki Mahsan
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7397
Subject(s) - mathematics , stability (learning theory) , interval (graph theory) , function (biology) , order (exchange) , control theory (sociology) , set (abstract data type) , fractional order system , value (mathematics) , range (aeronautics) , class (philosophy) , mathematical analysis , fractional calculus , combinatorics , control (management) , computer science , statistics , materials science , finance , evolutionary biology , machine learning , artificial intelligence , economics , composite material , biology , programming language
In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this value set may change at some switching frequencies and the repetitive calculation of these vertices at switching frequencies leads to additional calculations. In this study initially, new necessary and sufficient conditions are proposed to check the robust stability of a delayed fractional order closed loop system. Then, a novel robust stability testing function is presented based on some vertices, which are fixed for all positive frequencies. Therefore, no additional calculation is needed to obtain the outer vertices of the characteristic function value set for any pair of the switching frequencies. Also, a finite frequency range is presented to reduce the computational cost noticeably. Eventually, three numerical examples are given to verify the efficiency of the results of this paper.