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Liao, F; Yu, X; Deng, J (2017)
Publisher: SpringerOpen
Languages: English
Types: Article
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.
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    • 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)
    • 11. Cao, J, Zhong, S: New delay-dependent condition for absolute stability of Lurie control systems with multiple time-delays and nonlinearities. Appl. Math. Comput. 194(1), 250-258 (2007)
    • 12. Nam, PT, Pathirana, PN: Improvement on delay dependent absolute stability of Lurie control systems with multiple time delays. Appl. Math. Comput. 216(3), 1024-1027 (2010)
    • 13. Daryoush, BS, Soheila, DC: Improvement on delay dependent absolute stability of Lurie control systems with multiple time-delays and nonlinearities. World J. Model. Simul. 10(1), 20-26 (2014)
    • 14. Shatyrko, A, Diblík, J, Khusainov, D, Ru˚žicˇková, M: Stabilization of Lur'e-type nonlinear control systems by Lyapunov-Krasovskii functionals. Adv. Differ. Equ. 2012, 229 (2012)
    • 15. Wang, T-C, Wang, Y-C, Hong, L-R: Absolute stability for Lurie control system with unbound time delays. J. China Univ. Min. Technol. 14(1), 67-69 (2005)
    • 16. Zeng, H-B, He, Y, Wu, M, Feng, Z-Y: New absolute stability criteria for Lurie nonlinear systems with time-varying delay. Control Decis. 25(3), 346-350 (2010)
    • 17. Liu, P-L: Delayed decomposition approach to the robust absolute stability of a Lur'e control system with time-varying delay. Appl. Math. Model. 40(3), 2333-2345 (2016)
    • 18. Shatyrko, AV, Khusainov, DY: Absolute interval stability of indirect regulating systems of neutral type. J. Autom. Inf. Sci. 42(6), 43-54 (2010)
    • 19. Shatyrko, AV, Khusainov, DY, Diblik, J, Baštinec, J, Rivolova, A: Estimates of perturbation of nonlinear indirect interval control system of neutral type. J. Autom. Inf. Sci. 43(1), 13-28 (2011)
    • 20. Shatyrko, A, van Nooijen, RRP, Kolechkina, A, Khusainov, D: Stabilization of neutral-type indirect control systems to absolute stability state. Adv. Differ. Equ. 2015, 64 (2015)
    • 21. Liao, F-C, Li, A-G, Sun, F-B: Absolute stability of Lurie systems and Lurie large-scale systems with multiple operators and unbounded coefficients. J. Univ. Sci. Technol. B 31(11), 1472-1479 (2009)
    • 22. Wang, D, Liao, F: Absolute stability of Lurie direct control systems with time-varying coefficients and multiple nonlinearities. Appl. Math. Comput. 219(9), 4465-4473 (2013)
    • 23. Liao, F, Wang, D: Absolute stability criteria for large-scale Lurie direct control systems with time-varying coefficients. Sci. World J. 2014, Article ID 631604 (2014). doi:10.1155/2014/631604
    • 24. Burton, TA: Uniform asymptotical stability in functional differential equations. Proc. Am. Math. Soc. 68(2), 195-199 (1978)
    • 25. Burton, TA: Stability and Periodic Solutions of Ordinary and Functional Differential Equations. Academic Press, New York (1985)
    • 26. Lefschetz, S: Stability of Nonlinear Control Systems. Academic Press, New York (1965)
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