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A Computing Approach for Delay Margin of Linear Fractional‐Order Retarded Systems with Commensurate Time Delays
Author(s) -
Gao Zhe,
Liao Xiaozhong
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.834
Subject(s) - eigenvalues and eigenvectors , margin (machine learning) , mathematics , infinity , matrix (chemical analysis) , function (biology) , order (exchange) , control theory (sociology) , mathematical analysis , computer science , physics , control (management) , materials science , finance , quantum mechanics , machine learning , evolutionary biology , artificial intelligence , economics , composite material , biology
This paper proposes a computing approach for the delay margin of fractional‐order retarded systems with commensurate time delays. By the O rlando formula, a matrix constructed by the coefficients and commensurate fractional‐order of the characteristic function is defined. By calculating the eigenvalues of this matrix, the existence conditions and computing approach are proposed. If the matrix has some positive real eigenvalues, a finite delay margin exists. If the matrix has no positive real eigenvalue, the delay margin is infinity and the system is stable, independent of the delay margin. Finally, a numerical example and simulation results are given to demonstrate the effectiveness of this approach.