Absolute stability of time-delay systems with sector-bounded nonlinearity. (English) Zbl 1100.93519

Summary: This paper deals with the problem of absolute stability of time-delay systems with sector-bounded nonlinearity. Some new delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria. Numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result.


93D10 Popov-type stability of feedback systems
93C23 Control/observation systems governed by functional-differential equations
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[1] Aizerman, M. A.; Gantmacher, F. R., Absolute stability of regulator systems (1964), Holden-Day: Holden-Day San Francisco, CA · Zbl 0123.28401
[2] Bliman, P.-A., Lyapunov-Krasovskii functionals and frequency domain: delay-independent absolute stability criteria for delay systems, International Journal of Robust and Nonlinear Control, 11, 771-788 (2001) · Zbl 0992.93069
[3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[4] Gan, Z. X.; Ge, W. G., Lyapunov functional for multiple delay general Lur’e control systems with multiple non-linearities, Journal of Mathematics Analysis and Applications, 259, 596-608 (2001) · Zbl 0995.93041
[6] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (2003), Birkhäuser: Birkhäuser Boston · Zbl 1039.34067
[7] Hale, J. K.; Verduyn Lunel, S. M., Introduction to functional differential equations (1993), Springer: Springer New York · Zbl 0787.34002
[8] Han, Q.-L., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723 (2002) · Zbl 1020.93016
[9] He, Y.; Wu, M., Absolute stability for multiple delay general Lur’e control systems with multiple nonlinearities, Journal of Computational and Applied Mathematics, 159, 241-248 (2003) · Zbl 1032.93062
[10] Khalil, H. K., Nonlinear systems (1996), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ · Zbl 0626.34052
[11] Li, X.-J., On the absolute stability of systems with time lags, Chinese Mathematics, 4, 609-626 (1963)
[12] Liao, X. X., Absolute stability of nonlinear control systems (1993), Science Press: Science Press Beijing
[13] Lur’e, A. I., Some nonlinear problems in the theory of automatic control (1957), H.M. Stationery Office: H.M. Stationery Office London
[14] Popov, V. M., Hyperstability of control systems (1973), Springer: Springer New York, NY · Zbl 0276.93033
[15] Popov, V. M.; Halanay, A., About stability of non-linear controlled systems with delay, Automation and Remote Control, 23, 849-851 (1962)
[16] Somolines, A., Stability of Lurie type functional equations, Journal of Differential Equations, 26, 191-199 (1977)
[18] Yakubovich, V. A.; Leonov, G. A.; Gelig, A. Kh., Stability of stationary sets in control systems with discontinuous nonlinearities (2004), World Scientific: World Scientific Singapore · Zbl 1054.93002
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