zbMATH — the first resource for mathematics

BIBO stabilization for system with multiple mixed delays and nonlinear perturbations. (English) Zbl 1245.93114
Summary: The problem of BIBO stabilization for multiple mixed time-delayed control system with nonlinear perturbations is studied in this paper. The new delay-dependent BIBO stabilization criteria are derived by the Lyapunov functional and given in terms of existence of a positive definite solution to an auxiliary algebraic Riccati matrix equation. The robust quadratic stability for such system is also discussed. The work of this paper will extend the results of some references.

93D15 Stabilization of systems by feedback
93C73 Perturbations in control/observation systems
93C23 Control/observation systems governed by functional-differential equations
34K20 Stability theory of functional-differential equations
Full Text: DOI
[1] Zhou, T.J.; Liu, Y.R.; Liu, Y.H., Existence and global exponential stability of periodic solution for discrete-time BAM neural networks, Appl. math. comput., 182, 2, 1341-1354, (2006) · Zbl 1149.39302
[2] Sun, Y.J., Duality between observation and output feedback for linear systems with multiple time delays, Chaos soliton fract, 33, 3, 879-884, (2007) · Zbl 1136.93022
[3] Park, J.H.; Cho, H.J., A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Chaos soliton fract, 33, 2, 436-442, (2007) · Zbl 1142.34379
[4] Song, Y.L.; Peng, Y.H., Stability and bifurcation analysis on a logistic model with discrete and distributed delays, Appl. math. comput., 181, 2, 1745-1757, (2006) · Zbl 1161.34056
[5] Xu, R.; Chaplain, M.A.J., Persistence and attractivity in an N-species ratio-dependent predator – prey system with distributed time delays, Appl. math. comput., 131, 1, 59-80, (2002) · Zbl 1043.34088
[6] Chen, F.D., On a nonlinear nonautonomous predator – prey model with diffusion and distributed delay, J. comput. appl. math., 18, 1, 33-49, (2005) · Zbl 1061.92058
[7] Kotsios, S., A note on BIBO stability of bilinear systems, J. franklin inst., 332, 6, 755-760, (1995) · Zbl 0852.93083
[8] Bose, T.; Chen, M.Q., BIBO stability of the discrete bilinear system, Digital signal process., 5, 3, 160-166, (1995)
[9] Fornasini, E.; Valcher, M.E., On some connections between bilinear input/output maps and 2D systems, Nonlinear anal., 30, 4, 1995-2005, (1997) · Zbl 0895.93004
[10] 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
[11] Zhong, S.M.; Huang, Y.Q., BIBO stabilization of nonlinear system with time-delay, J. UEST China, 29, 6, 655-657, (2000)
[12] Xu, D.Y.; Zhong, S.M., The BIBO stabilization of multivariable feedback systems, J. UEST China, 24, 1, 90-96, (1995)
[13] Xu, D.Y.; Zhong, S.M., BIBO stabilization of large-scale systems, Cont. theory appl., 12, 6, 758-763, (1995)
[14] Li, P.; Zhong, S.M., BIBO stabilization of time-delayed system with nonlinear perturbation, Appl. math. comput., (2007)
[15] You, K.H.; Lee, E.B., BIBO stability integral (L∞-gain) for second-order systems with numerator dynamics, Automatica, 36, 1693-1699, (2000) · Zbl 0966.93103
[16] Kotsios, S.; Feely, O., A BIBO stability theorem for a two-dimensional feedback discrete system with discontinuities, J. franklin inst., 335B, 533-537, (1998) · Zbl 0905.93037
[17] Shahruz, S.M.; Sakyaman, N.A., How to have narrow-stripe semiconductor lasers self-pulsate, Appl. math. comput., 130, 11-27, (2002) · Zbl 1021.78007
[18] 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.