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A discrete delay decomposition approach to stability of linear retarded and neutral systems. (English) Zbl 1158.93385
Summary: This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [{\it Q.-L. Han}, Automatica, 41, No. 12, 2171--2176 (2005; Zbl 1100.93519); Int. J. Syst. Sci. 36, No. 8, 469--475 (2005; Zbl 1093.34037)]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in [Han (loc. cit.)] cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.

93D09Robust stability of control systems
34K40Neutral functional-differential equations
Full Text: DOI
[1] Bellman, R.; Cooke, K. L.: Differential-difference equations, (1963) · Zbl 0105.06402
[2] Brayton, R. K.: Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type, Quarterly of applied mathematics 24, 215-224 (1966) · Zbl 0143.30701
[3] Chen, J.: On computing the maximal delay intervals for stability of linear delay systems, IEEE transactions on automatic control 40, 1087-1093 (1995) · Zbl 0840.93074 · doi:10.1109/9.388690
[4] Chen, J.; Gu, G.; Nett, C. N.: A new method for computing delay margins for stability of linear delay systems, Systems & control letters 26, 107-117 (1995) · Zbl 0877.93117 · doi:10.1016/0167-6911(94)00111-8
[5] Chiasson, J. N.: A method for computing the interval of delay values for which a differential-delay system is stable, IEEE transactions on automatic control 33, 1176-1178 (1985) · Zbl 0668.34074 · doi:10.1109/9.14446
[6] Fridman, E.; Shaked, U.: A descriptor system approach to control of linear time-delay systems, IEEE transactions on automatic control 47, 253-270 (2002) · Zbl 1006.93021
[7] Gouaisbaut, F., & Peaucelle, D. (2006). Delay-dependent stability analysis of linear time delay systems. In The 6th IFAC workshop on time-delay systems · Zbl 1293.93589
[8] Gu, K.: A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, International journal of control 74, 967-976 (2001) · Zbl 1015.93053 · doi:10.1080/00207170110047190
[9] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems, (2003) · Zbl 1039.34067
[10] Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations, (1993) · Zbl 0787.34002
[11] Hale, J. K.; Infante, E. F.; Tsen, F. S. P.: Stability in linear delay equations, Journal of mathematical analysis and applications 105, 533-555 (1985) · Zbl 0569.34061 · doi:10.1016/0022-247X(85)90068-X
[12] Han, Q. -L.: Robust stability of uncertain delay-differential systems of neutral type, Automatica 38, 719-723 (2002) · Zbl 1020.93016 · doi:10.1016/S0005-1098(01)00250-3
[13] Han, Q. -L.: Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica 41, 2171-2176 (2005) · Zbl 1100.93519 · doi:10.1016/j.automatica.2005.08.005
[14] Han, Q. -L.: A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices, International journal of systems science 36, 469-475 (2005) · Zbl 1093.34037 · doi:10.1080/00207720500157437
[15] Han, Q. -L.; Yue, D.: Absolute stability of Lur’e systems with time-varying delay, IET control theory and applications 1, 854-859 (2007)
[16] He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE transactions on automatic control 49, 828-832 (2004)
[17] Hertz, D.; Jury, E. J.; Zeheb, E.: Stability independent and dependent of delay for delay differential systems, Journal of the franklin institute 318, 143-150 (1984) · Zbl 0552.34066 · doi:10.1016/0016-0032(84)90038-3
[18] Kolmanovskii, V.; Myshkis, A.: Introduction to the theory and applications of functional differential equations, (1999) · Zbl 0917.34001
[19] Lien, C. -H.; Chen, J. -D.: Discrete-delay-independent and discrete-delay-dependent criteria for a class of neutral systems, ASME journal of dynamic systems, measurement and control 125, 33-41 (2003)
[20] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S.: Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control 74, 1447-1455 (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116
[21] Niculescu, S. -I.: Delay effects on stability: A robust control approach, (2001) · Zbl 0997.93001
[22] Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE transactions on automatic control 44, 876-877 (1999) · Zbl 0957.34069 · doi:10.1109/9.754838
[23] Wu, M.; He, Y.; She, J. H.: New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE transactions on automatic control 49, 2267-2271 (2004)