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)
Finite-time $H_{\infty }$ control for a class of discrete-time switched time-delay systems with quantized feedback. (English) Zbl 1263.93072
Summary: This paper is concerned with the finite-time quantized $H_{\infty }$ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed $H_{\infty }$ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

MSC:
93B36$H^\infty$-control
93C55Discrete-time control systems
93C30Control systems governed by other functional relations
WorldCat.org
Full Text: DOI
References:
[1] Elia, N.; Mitter, S. K.: Stabilization of linear systems with limited information, IEEE trans automat control 46, No. 9, 1384-1400 (2001) · Zbl 1059.93521 · doi:10.1109/9.948466 · http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=948466
[2] Fu, M.; Xie, L.: The sector bound approach to quantized feedback control, IEEE trans automat control 50, No. 11, 1698-1711 (2005)
[3] Hespanha JP, Morse AS. Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE conference on decision control, vol. 3; 1999. p. 2655 -- 60.
[4] Decarlo, R. A.; Branicky, M. S.; Petterssoon, S.; Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems, Proc IEEE 88, No. 7, 1069-1082 (2008)
[5] Sun, Z.; Ge, S. S.: Analysis and synthesis of switched linear control systems, Automatica 41, No. 2, 181-195 (2005) · Zbl 1074.93025 · doi:10.1016/j.automatica.2004.09.015
[6] Zhai G, Hu B, Yasuda K, Michel AN. Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach. In: Proceedings of the 2000 American control conference, vol. 1; 2000. p. 200 -- 4. · Zbl 1022.93043
[7] Ding, D.; Yang, G.: H$\infty $ static output feedback control for discrete-time switched linear systems with average Dwell time, IET control theory appl 4, No. 3, 381-390 (2010)
[8] Zhang, D.; Yu, L.; Zhang, W.: Delay-dependent fault detection for switched systems with time-varying delays --- the average Dwell dime approach, Signal process 91, No. 4, 832-840 (2011) · Zbl 1217.94081 · doi:10.1016/j.sigpro.2010.08.016
[9] Zhang, L.; Shi, P.: Stability, l2-gain and asynchronous H$\infty $ control of discrete-time switched systems with average Dwell time, IEEE trans automat control 54, No. 9, 2193-2200 (2009)
[10] Zhang, L.; Gao, H.: Asynchronously switched control of switched linear systems with average Dwell time, Automatica 46, No. 5, 953-958 (2010) · Zbl 1191.93068 · doi:10.1016/j.automatica.2010.02.021
[11] Liberzon, D.; Morse, A. S.: Basic problems in stability and design of switched systems, IEEE control syst mag 19, No. 5, 59-70 (1999)
[12] Amato, F.; Ariola, M.; Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica 37, No. 9, 1459-1463 (2001) · Zbl 0983.93060 · doi:10.1016/S0005-1098(01)00087-5
[13] Amato, F.; Ariola, M.; Cosentino, C.: Finite-time control of discrete-time linear systems: analysis and design conditions, Automatica 46, No. 5, 919-924 (2010) · Zbl 1191.93099 · doi:10.1016/j.automatica.2010.02.008
[14] Garcia, G.; Tarbouriech, S.; Bernussou, J.: Finite-time stabilization of linear time-varying continuous systems, IEEE trans automat control 54, No. 2, 364-369 (2009)
[15] Feng, J.; Wu, Z.; Sun, J.: Finite-time control of linear singular systems with parametric uncertainties and disturbances, Acta automat sinica 31, No. 4, 634-637 (2005)
[16] Meng, Q.; Shen, Y.: Finite-time H$\infty $ control for linear continuous system with norm-bounded disturbance, Commun nonlinear sci numer simul 14, No. 4, 1043-1049 (2009) · Zbl 1221.93066 · doi:10.1016/j.cnsns.2008.03.010
[17] Dorato P. Short time stability in linear time-varying systems. In: Proceedings of the IRE international convention record part 4, New York; 1961. p. 83 -- 7.
[18] Weiss, L.; Infante, E. F.: Finite time stability under perturbing forces and on product spaces, IEEE trans automat control 12, No. 1, 54-59 (1967) · Zbl 0168.33903
[19] Du H, Lin X, Li S. Finite-time stability and stabilization of switched linear systems. In: Proceedings of the joint 48th IEEE conference on decision and control and 28th chinese control conference, 2009. p. 1938 -- 43.
[20] Branicky, M. S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE trans automat control 43, No. 4, 475-482 (1998) · Zbl 0904.93036 · doi:10.1109/9.664150
[21] Daafouz, J.; Riedinger, P.; Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach, IEEE trans automat control 47, No. 11, 1883-1887 (2002)
[22] Xiang, W.; Xiao, J.: H$\infty $ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance, J franklin inst 348, No. 2, 331-352 (2011) · Zbl 1214.93043 · doi:10.1016/j.jfranklin.2010.12.001
[23] Ferrari-Trecate, G.; Cuzzola, F. A.; Mignone, D.; Morari, M.: Analysis of discrete-time piecewise affine and hybrid systems, Automatica 38, No. 12, 2139-2146 (2002) · Zbl 1010.93090 · doi:10.1016/S0005-1098(02)00142-5
[24] Huijun, Gao; Changhong, Wang: A delay-dependent approach to robust H$\infty $ filtering for uncertain discrete-time state-delayed systems, IEEE trans automat control 52, No. 6, 1631-1640 (2004) · Zbl 1052.93056
[25] Wen-An, Zhang; Li, Yu: 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
[26] Ma Dan, Dimirovski Georgi M, Liu Tao, Zhao Jun. Robust exponential stabilization of switched systems with network time-varying delays and packet dropout. In: Proceedings of the 27th Chinese control conference, Kunming, PR China, July 16 -- 18, 2008. p. 96 -- 100.