×

Non-fragile control for nonlinear networked control systems with long time-delay. (English) Zbl 1186.93031

Summary: This paper considers the non-fragile control problem for uncertain nonlinear networked control systems (NCSs) with long time-delay and controller gain perturbations. Firstly, the NCS model with random long time-delay is transformed into a discrete-time system model with uncertain parameters. Then, the Lyapunov stability theory and the linear matrix inequality (LMI) approach are applied to design a non-fragile controller, which results in the closed-loop system being asymptotically stable and the system’s cost function value being less than a determinate upper bound. At the same time, the existence condition and the design approach of a non-fragile controller are presented. Finally, simulation examples are employed to verify the validity of the proposed control algorithm.

MSC:

93B52 Feedback control
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Yue, D.; Peng, C.; Tang, G.-Y., Guaranteed cost control of linear systems over networks with state and input quantisations, IEE Proceedings: control theory and applications, 155, 658-664, (2006)
[2] Savkin, A.V., Analysis and synthesis of networked control systems: topological entropy, observability, robustness and optimal control, Automatica, 42, 51-62, (2006) · Zbl 1121.93321
[3] Yue, D.; Han, Q.-L.; Lam, J., Network-based robust \(H_\infty\) control of systems with uncertainty, Automatica, 41, 999-1007, (2005) · Zbl 1091.93007
[4] Yu, L.; Chu, J., LMI approach to guaranteed cost control of linear uncertain time-delay systems, Automatica, 35, 1155-1159, (1999) · Zbl 1041.93530
[5] Yu, L.; Gao, F., Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays, Journal of the franklin institute, 338, 101-110, (2001) · Zbl 0998.93512
[6] Keel, L.H.; Bhattacharyya, S.P., Robust, fragile, or optimal?, IEEE transactions on automatic control, 42, 1098-1105, (1997) · Zbl 0900.93075
[7] Xie, N.; Tang, G.-Y., Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems, Nonlinear analysis, theory, methods and applications, 64, 2084-2097, (2006) · Zbl 1161.93315
[8] Yue, D.; Lam, J., Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays, Optimal control applications and methods, 26, 85-105, (2005)
[9] Yee, J.S.; Wang, J.L.; Yang, G.H., LMI approach to non-fragile guaranteed cost control of uncertain discrete time-delay systems, Asian journal of control, 3, 226-233, (2001)
[10] Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system, Journal of optimization theory and applications and applications, 46, 399-408, (1985) · Zbl 0549.93045
[11] Albert, A., Conditions for positive and non-negative definiteness in terms of pseudoinverses, SIAM journal on applied mathematics, 17, 434-440, (1969) · Zbl 0265.15002
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.