# 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)
${H}_{\infty }$ control of a class of networked control systems with time delay and packet dropout. (English) Zbl 1216.93042
Summary: This paper studies the ${H}_{\infty }$ control issue for a class of Networked Control Systems (NCSs) with time delay and packet dropout. The state feedback closed-loop NCS is modeled as a discrete-time switching system. Through using a Lyapunov function, a sufficient condition is obtained, under which the system is exponential stability with a desired ${H}_{\infty }$ disturbance attenuation level. The designed ${H}_{\infty }$ controller is obtained by solving a set of linear matrix inequalities. An illustrative example is presented to demonstrate the effectiveness of the proposed method.
##### MSC:
 93B36 ${H}^{\infty }$-control 93B52 Feedback control 93D20 Asymptotic stability of control systems
##### References:
 [1] Hu, L. S.; Bai, T.; Shi, P.; Wu, Z. M.: Sampled-data control of networked linear control systems, Automatica 43, No. 5, 903-911 (2007) · Zbl 1117.93044 · doi:10.1016/j.automatica.2006.11.015 [2] Shi, Y.; Fang, H.; Yan, M.: Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs, Int. J. Robust nonlinear contr. 19, No. 18, 1976-1992 (2009) · Zbl 1192.93118 · doi:10.1002/rnc.1390 [3] Shi, Y.; Fang, H.: Kalman filter based identification for systems with randomly missing measurements in a network environment, Int. J. Contr. 83, No. 3, 538-551 (2010) [4] B. Yu, Y. Shi, J. Huang, Modified generalized predictive control of networked systems with application to a hydraulic position control system, J. Dyn. Syst. Meas. Control 133 (2) (in press). [5] Gao, H. J.; Chen, T.; Lam, J.: A new delay system approach to network-based control, Automatica 44, No. 1, 39-52 (2008) · Zbl 1138.93375 · doi:10.1016/j.automatica.2007.04.020 [6] Shi, Y.; Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains, IEEE trans. Automat. contr. 54, No. 8, 1966-1972 (2009) [7] Zhang, Y.; Tang, G. Y.; Hu, N. P.: Non-fragile H$\infty$ control for nonlinear networked control systems with long time-delay, Comput. math. Appl. 57, No. 12, 1630-1637 (2009) · Zbl 1186.93031 · doi:10.1016/j.camwa.2009.03.053 [8] Zhang, L.; Shi, Y.; Chen, T.; Huang, B.: A new method for stabilization of networked control systems with random delays, IEEE trans. Automat. contr. 50, No. 8, 1177-1181 (2005) [9] Y. Shi, B. Yu, Robust mixed H2/Hnbsp; control of networked control systems with random time delays in both forward and backward communication links, Automatica (in press). [10] Lin, H.; Antsaklis, P. J.: Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach, Int. J. Contr. 78, No. 18, 1447-1458 (2005) · Zbl 1122.93357 · doi:10.1080/00207170500329182 [11] Zhang, W. A.; Yu, L.: Output feedback stabilization of networked control systems with packet dropouts, IEEE trans. Automat. contr. 52, No. 9, 1705-1710 (2007) [12] Xiong, J.; Lam, J.: Stabilization of linear systems over networks with bounded packet loss, Automatica 43, No. 1, 80-87 (2007) · Zbl 1140.93383 · doi:10.1016/j.automatica.2006.07.017 [13] Zhang, W. A.; Yu, L.: Modelling and control of networked control systems with both network-induced delay and packet-dropout, Automatica 44, No. 12, 3206-3210 (2008) · Zbl 1153.93321 · doi:10.1016/j.automatica.2008.09.001 [14] Gao, J.; Huang, B.; Wang, Z.: Lmi-based robust H$\infty$ control of uncertain linear jump systems with time-delays, Automatica 37, No. 7, 1141-1146 (2001) · Zbl 0989.93029 · doi:10.1016/S0005-1098(01)00046-2 [15] Li, M.; Zhou, W.; Lu, H.; Fang, J.: Robust H$\infty$ control for a generic linear rational expectations model of economy, Appl. math. Comput. 216, No. 7, 2145-2154 (2010) · Zbl 1193.93092 · doi:10.1016/j.amc.2010.03.049 [16] Lien, C. H.; Yu, K. W.; Lin, Y. F.; Chung, Y. J.; Chung, L. Y.: Robust reliable H$\infty$ control for uncertain nonlinear systems via lmi approach, Appl. math. Comput. 198, No. 1, 453-462 (2008) · Zbl 1141.93322 · doi:10.1016/j.amc.2007.08.085 [17] Peng, C.; Yue, D.; Tian, Y. C.: Delay distribution based robust H$\infty$ control of networked control systems with uncertainties, Asian J. Contr. 12, No. 1, 46-57 (2009) [18] Jia, T. G.; Niu, Y. G.; Wang, X. Y.: H$\infty$ control for networked systems with data packet dropout, Asian J. Contr. 8, No. 2, 198-203 (2010) [19] Li, J. G.; Yuan, J. Q.; Lu, J. G.: Observer-based H$\infty$ control for networked nonlinear systems with random packet losses, ISA trans. 49, No. 1, 39-46 (2010) [20] G. Zhai, B. Hu, K. Yasuda, A.N. Michel, Qualitative analysis of discrete-time switched systems, in: Proceedings of 2002 American Control Conference, USA, 2002, pp. 1880 – 1885. [21] Zhang, W.; Branicky, M.; Phillips, S.: Stability of networked control systems, IEEE contr. Syst. mag. NY 21, No. 1, 84-99 (2001)