zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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.

MSC:
 93D15 Stabilization of systems by feedback 93C73 Perturbations in control systems 93C23 Systems governed by functional-differential equations 34K20 Stability theory of functional-differential equations
Full Text:
References:
 [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, No. 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, No. 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, No. 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, No. 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, No. 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, No. 1, 33-49 (2005) · Zbl 1061.92058 [7] Kotsios, S.: A note on BIBO stability of bilinear systems. J. franklin inst. 332, No. 6, 755-760 (1995) · Zbl 0852.93083 [8] Bose, T.; Chen, M. Q.: BIBO stability of the discrete bilinear system. Digital signal process. 5, No. 3, 160-166 (1995) [9] Fornasini, E.; Valcher, M. E.: On some connections between bilinear input/output maps and 2D systems. Nonlinear anal. 30, No. 4, 1995-2005 (1997) · Zbl 0850.93498 [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, No. 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, No. 6, 655-657 (2000) [12] Xu, D. Y.; Zhong, S. M.: The BIBO stabilization of multivariable feedback systems. J. UEST China 24, No. 1, 90-96 (1995) [13] Xu, D. Y.; Zhong, S. M.: BIBO stabilization of large-scale systems. Cont. theory appl. 12, No. 6, 758-763 (1995) [14] Li, P.; Zhong, S. M.: BIBO stabilization of time-delayed system with nonlinear perturbation. Appl. math. Comput. (2007) · Zbl 1130.93046 [15] You, K. H.; Lee, E. B.: BIBO stability integral (L$\infty$-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, No. 2, 265-276 (1993) · Zbl 0781.93074