×

zbMATH — the first resource for mathematics

Stabilization of nonlinear networked probabilistic interval delay systems with sensor random packet dropout. (English) Zbl 1286.93197
Summary: In this paper, the problem of stabilization for nonlinear networked systems with probabilistic interval delay and sensor random packet dropout is investigated. By employing the information of probabilistic distribution of time-varying delay and considering random sensor packet dropout with compensation, the nonlinear stochastic delayed system model is established. Based on the obtained model, by choosing an appropriate Lyapunov function and utilizing a new discrete Jensen-type inequality, sufficient conditions are derived to obtain the relation of the maximum allowable delay bound, delay interval occurrence rate and packet dropout rate to the stochastic stability of nonlinear networked control systems. Two kinds of design procedures for output feedback controller are also presented in terms of solving corresponding linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness and applicability of proposed techniques.

MSC:
93E15 Stochastic stability in control theory
93C55 Discrete-time control/observation systems
93C65 Discrete event control/observation systems
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zhang, Stability of networked control systems, IEEE Control Syst. Mag. 21 pp 84– (2001) · doi:10.1109/37.898794
[2] Hespanha, A survey of recent results in networked control systems, Proc. IEEE 95 pp 138– (2007) · doi:10.1109/JPROC.2006.887288
[3] Kim, Maximum allowable delay bounds of networked control systems, Control Eng. Practice 11 pp 1301– (2003) · doi:10.1016/S0967-0661(02)00238-1
[4] Yang, H control for networked systems with random communication delays, IEEE Trans. Autom. Control 51 pp 511– (2006) · Zbl 1366.93167 · doi:10.1109/TAC.2005.864207
[5] Gao, Stabilization of networked control systems with a new delay characterization, IEEE Trans. Autom. Control 53 pp 2142– (2008) · Zbl 1367.93696 · doi:10.1109/TAC.2008.930190
[6] Zhang , Y. H. J. Fang S. Fu Observer-based fault detection for nonlinear networked systems with random dropout and time-varying delay 4278 4282
[7] Peng, Delay distribution based robust H control of networked control systems with uncertainties, Asian J. Control 12 (1) pp 46– (2010)
[8] Shen, On nonlinear H filtering for discrete-time stochastic systems with missing measurements, IEEE Trans. Autom. Control 53 pp 2170– (2008) · Zbl 1367.93659 · doi:10.1109/TAC.2008.930199
[9] Wu, Design of networked control systems with packet dropouts, IEEE Trans. Autom. Control 52 pp 1314– (2007) · Zbl 1366.93215 · doi:10.1109/TAC.2007.900839
[10] Fang, Sampled-data H control for networked systems with random packet dropouts, Asian J. Control 12 (5) pp 549– (2010)
[11] Yue, Network-based robust H control of systems with uncertainty, Automatica 4 (6) pp 999– (2005) · Zbl 1091.93007 · doi:10.1016/j.automatica.2004.12.011
[12] Yu, Stabilization of networked control systems with data packet dropout via switched system approach, Proc. 43rd IEEE Conf. Decis. Control 43 pp 3539– (2004)
[13] Zhang, Modelling and control of networked control systems with both network-induced delay and packet-dropout, Automatica 44 (12) pp 3206– (2008) · Zbl 1153.93321 · doi:10.1016/j.automatica.2008.09.001
[14] Han, Absolute stability for time delay systems with sector-bound nonlinearity, Auto-matica 41 (12) pp 2171– (2005)
[15] Lam, H and L2/L infinity model reduction or system input with sector nonlinearities, J. Optim. Theory Appl. 125 (1) pp 137– (2005) · Zbl 1062.93020 · doi:10.1007/s10957-004-1714-6
[16] Wang, H-infinity filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica 44 (5) pp 1268– (2008) · Zbl 1283.93284 · doi:10.1016/j.automatica.2007.09.016
[17] Nilsson, Stochastic analysis and control of real-time systems with random time delays, Automatica 34 pp 57– (1998) · Zbl 0908.93073 · doi:10.1016/S0005-1098(97)00170-2
[18] Gao, New results on stability of discrete-time systems with time-varying state delay, IEEE Trans. Autom. Control 52 (2) pp 328– (2007) · Zbl 1366.39011 · doi:10.1109/TAC.2006.890320
[19] EI, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Trans. Autom. Control 42 (8) pp 1171– (1997) · Zbl 0887.93017 · doi:10.1109/9.618250
[20] Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777
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.