zbMATH — the first resource for mathematics

BIBO stabilization of time-delayed system with nonlinear perturbation. (English) Zbl 1130.93046
Summary: Time-delayed control system with the nonlinear perturbation is considered. Novel BIBO stabilization criteria are established by the Lyapunov functional and formulated in terms of existence of a positive definite solution to an auxiliary algebraic Riccati matrix equation. The robust quadratic stability for such systems is also discussed. A numerical example is given to illustrate the effectiveness of our result.

93D25 Input-output approaches in control theory
93D30 Lyapunov and storage functions
93D09 Robust stability
93C73 Perturbations in control/observation systems
34K35 Control problems for functional-differential equations
Full Text: DOI
[1] Chen, F.D., Permanence of a discrete N-species cooperation system with time delays and feedback controls, Appl. math. comput., 186, 1, 23-29, (2007) · Zbl 1113.93063
[2] Corless, M.; Garofalo, F.; Gilelmo, L., New results on composite control of singularly perturbed uncertain linear systems, Automatica, 29, 2, 387-400, (1993) · Zbl 0772.93062
[3] Sen, S.; Datta, K.B., Stability bounds of singularly perturbed systems, IEEE trans. automat. control, 38, 2, 302-304, (1993) · Zbl 0774.93053
[4] Garcia, G.; Bernussou, J., H2 guaranteed cost control for singularly perturbed uncertain systems, IEEE trans. automat. control, 43, 9, 1323-1329, (1998) · Zbl 0957.93057
[5] Shi, P.; Dragan, V., Asymptotic H1 control of singularly perturbed systems with parametric uncertainties, IEEE trans. automat. control, 44, 9, 1738-1742, (1999) · Zbl 0958.93066
[6] Singh, H.; Brown, R.H.; Naidu, D.S.; Heinen, J.A., Robust stability of singularly perturbed state feedback systems using unified approach, IEE proc. control theory appl., 148, 5, 391-396, (2001)
[7] Xu, D.Y.; Zhong, S.M., The BIBO stabilization of multivariable feedback systems, J. UEST China, 24, 1, 90-96, (1995)
[8] Cao, K.C.; Zhong, S.M.; Liu, B.S., BIBO and robust stabilization for system with time-delay and nonlinear perturbations, J. UEST China, 32, 6, 787-789, (2003) · Zbl 1078.93050
[9] Guan, Z.H.; Wen, X.C.; Liu, Y.Q., Variation of the parameters formula and the problem of BIBO for singular measure differential systems with impulse effect, Appl. math. comput., 60, 2-3, 153-169, (1994) · Zbl 0820.35153
[10] Partington, R.J.; Bonnet, C., H∞ and BIBO stabilization of delay systems of neutral type, Syst. control lett., 52, 3-4, 283-288, (2004) · Zbl 1157.93367
[11] Shahruz, S.M.; Sakyaman, N.A., How to have narrow-stripe semiconductor lasers self-pulsate, Appl. math. comput., 130, 1, 11-27, (2002) · Zbl 1021.78007
[12] Wu, H.; Mizukami, K., Robust stabilization of uncertain linear dynamical systems, Int. J. syst. sci., 24, 2, 265-276, (1993) · Zbl 0781.93074
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.