# 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)
State estimation and stabilization for nonlinear networked control systems with limited capacity channel. (English) Zbl 1231.93111
Summary: This paper investigates the control problem for nonlinear networked control systems with global Lipschitz nonlinearities subject to output quantization and data packet dropout. The system states are unavailable and the outputs are quantized in a logarithmic form before transmitted through the network. In the communication channel, two types of packet losses are considered simultaneously: (i) packet losses from sensor to controller and (ii) packet losses from controller to actuator, which are modeled as two independent Bernoulli distributed white sequences, respectively. Based on the proposed model, an observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and sufficient conditions for the existence of the controller are established. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique.
##### MSC:
 93E10 Estimation and detection in stochastic control 93E15 Stochastic stability 90B18 Communication networks (optimization) 93C55 Discrete-time control systems 93C10 Nonlinear control systems 93B07 Observability
##### References:
 [1] B. Azimi-Sadjadi, Stability of networked control systems in the presence of packet losses, Proceedings of IEEE Conference on Decision and Control, vol. 1, 2003, pp. 676–681. [2] Basin, M.; Rodriguez-Gonzalez, J.; Fridman, L.: Optimal and robust control for linear state-delay systems, Journal of the franklin institute 344, No. 6, 830-845 (2007) · Zbl 1119.49021 · doi:10.1016/j.jfranklin.2006.10.002 [3] Dong, H.; Wang, Z.; Gao, H.: Observer-based H$\infty$ control for systems with repeated scalar nonlinearities and multiple packet losses, International journal of robust and nonlinear control 20, No. 12, 1363-1378 (2010) · Zbl 1206.93035 · doi:10.1002/rnc.1519 [4] Dong, H.; Wang, Z.; Ho, D. W. C.; Gao, H.: Variance-constrained H$\infty$ filtering for a class of nonlinear time-varying systems with multiple missing measurements: the finite-horizon case, IEEE transactions on signal processing 58, No. 5, 2534-2543 (2010) [5] Gao, H.; Chen, T.: H$\infty$ estimation for uncertain systems with limited communication capacity, IEEE transactions on automatic control 52, No. 11, 2070-2084 (2007) [6] Gao, H.; Chen, T.: A new approach to quantized feedback control systems, Automatica 44, No. 2, 534-542 (2008) [7] He, X.; Wang, Z.; Ji, Y.; Zhou, D.: Fault detection for discrete-time systems in a networked environment, International journal of systems science 41, No. 8, 937-945 (2010) · Zbl 1213.93123 · doi:10.1080/00207720902974744 [8] Kim, D.; Park, P.; Ko, J.: Output-feedback H$\infty$ control of systems over communication networks using a deterministic switching system approach, Automatica 40, No. 7, 1205-1212 (2004) · Zbl 1056.93527 · doi:10.1016/j.automatica.2004.01.024 [9] Li, H.; Zhou, Q.; Chen, B.; Liu, H.: Parameter-dependent robust stability for uncertain Markovian jump systems with time delay, Journal of the franklin institute 348, No. 4, 738-748 (2011) · Zbl 1227.93126 · doi:10.1016/j.jfranklin.2011.02.002 [10] Liu, M.; Ho, D. W. C.; Niu, Y.: Stabilization of Markovian jump linear system over networks with random communication delay, Automatica 45, No. 2, 416-421 (2009) · Zbl 1158.93412 · doi:10.1016/j.automatica.2008.06.023 [11] Nahi, N.: Optimal recursive estimation with uncertain observation, IEEE transactions on information theory 15, No. 4, 457-462 (1969) · Zbl 0174.51102 · doi:10.1109/TIT.1969.1054329 [12] Niu, Y.; Jia, T.; Wang, X.; Yang, F.: Output-feedback control design for ncss subject to quantization and dropout, Information sciences 179, No. 21, 3804-3813 (2009) · Zbl 1171.93328 · doi:10.1016/j.ins.2009.07.006 [13] Shen, B.; Wang, Z.; Shu, H.; Wei, G.: On H$\infty$ nonlinear filtering for discrete-time stochastic systems with missing measurements, IEEE transactions on automatic control 53, No. 9, 2170-2180 (2008) [14] Shen, B.; Wang, Z.; Shu, H.; Wei, G.: Robust H$\infty$ finite-horizon filtering with randomly occurred nonlinearities and quantization effects, Automatica 46, No. 10, 1682-1688 (2010) [15] Wang, Z.; Ho, D. W. C.; Liu, X.: Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE transactions on automatic control 48, No. 7, 1254-1258 (2003) [16] Wang, Z.; Yang, F.; Ho, D. W. C.; Liu, X.: Robust H$\infty$ control for networked systems with random packet losses, IEEE transactions on systems, man, and cybernetics, part B 37, No. 4, 916-924 (2007) [17] Wu, L.; Shi, P.; Gao, H.: State estimation and sliding-mode control of Markovian jump singular systems, IEEE transactions on automatic control 55, No. 5, 1213-1219 (2010) [18] Wu, L.; Shi, P.; Gao, H.; Wang, C.: H$\infty$ filtering for 2D Markovian jump systems, Automatica 44, No. 7, 1849-1858 (2008) · Zbl 1149.93346 · doi:10.1016/j.automatica.2007.10.027 [19] Wu, L.; Wang, C.; Zeng, Q.: Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems, Journal of the franklin institute 345, No. 3, 233-253 (2008) · Zbl 1167.93326 · doi:10.1016/j.jfranklin.2007.09.001 [20] Yakubovich, V.: S-procedure in nonlinear control theory, Vestnik leningrad university 1, 62-77 (1971) · Zbl 0232.93010 [21] Yang, F.; Wang, Z.; Ho, D. W. C.; Gani, M.: Robust H$\infty$ control with missing measurements and time delays, IEEE transactions on automatic control 52, No. 9, 1666-1672 (2007) [22] Yang, F.; Wang, Z.; Hung, Y.; Gani, M.: H$\infty$ control for networked systems with random communication delays, IEEE transactions on automatic control 51, No. 3, 511-518 (2006) [23] Zhang, L.; Boukas, E.: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica 45, No. 2, 463-468 (2009) · Zbl 1158.93414 · doi:10.1016/j.automatica.2008.08.010 [24] Zhang, L.; Boukas, E.: Mode-dependent H$\infty$ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities, Automatica 45, No. 6, 1462-1467 (2009) · Zbl 1166.93378 · doi:10.1016/j.automatica.2009.02.002 [25] Zhang, L.; Shi, P.; Boukas, E.; Wang, C.: H$\infty$ control of switched linear discrete-time systems with polytopic uncertainties, Optimal control applications and methods 27, No. 5, 273-291 (2006) [26] Zhang, W.; Branicky, M.; Phillips, S.: Stability of networked control systems, IEEE control systems magazine 21, No. 1, 84-99 (2001)