Absolute stability of time-varying delay Lurie indirect control systems with unbounded coefficients

Article English OPEN
Liao, Fucheng ; Yu, Xiao ; Deng, Jiamei (2017)
  • Publisher: Springer Nature
  • Journal: Advances in Difference Equations
  • Related identifiers: doi: 10.1186/s13662-017-1094-5
  • Subject: Applied Mathematics | Algebra and Number Theory | Analysis

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative. Furthermore, the results are generalised to multiple nonlinearities. The derived criteria are especially suitable for time-varying delay Lurie indirect control systems with unbounded coefficients. The effectiveness of the proposed results is illustrated using simulation examples.
  • References (26)
    26 references, page 1 of 3

    1. Lur'e, AI, Postnikov, VN: On the theory of stability of control system. Prikl. Mat. Meh. 8(3), 283-286 (1944)

    2. Liberzon, MR: Essays on the absolute stability theory. Autom. Remote Control 67(10), 1610-1644 (2006)

    3. Gelig, AH, Leonov, GA, Fradkov, AL: Nonlinear Systems. Frequency and Matrix Inequalities. Fizmatlit, Moscow (2008)

    4. Lur'e, AI: Some Nonlinear Problems in the Theory of Automatic Control. H. M. Stationery Office, London (1957)

    5. Aizerman, MA, Gantmaher, FR: Absolute Stability of Regulator Systems. Holden-Day, San Francisco (1964)

    6. Xie, H: Theories and Applications of Absolute Stability. Science Press, Beijing (1986)

    7. Khusainov, DY, Shatyrko, AV: Absolute stability of multi-delay regulation systems. J. Autom. Inf. Sci. 27(3), 33-42 (1995)

    8. Chen, W-H, Guan, Z-H, Lu, X-M: Absolute stability of Lurie indirect control systems with multiple variable delays. Acta Math. Sin. 47(6), 1063-1070 (2004)

    9. Gan, Z-X, Ge, W-G: Absolute stability of a class of multiple nonlinear Lurie control systems with delay. Acta Math. Sin. 43(4), 633-638 (2000)

    10. Tian, J, Zhong, S, Xiong, L: Delay-dependent absolute stability of Lurie control systems with multiple time-delays. Appl. Math. Comput. 188(1), 379-384 (2007)

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