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)
$\cal H_{\infty}$ filtering for 2D Markovian jump systems. (English) Zbl 1149.93346
Summary: This paper is concerned with the problem of $\cal H_{\infty}$ filtering for 2D discrete Markovian jump systems. The mathematical model of 2D jump systems is established upon the well-known Roesser model. Our attention is focused on the design of a full-order filter, which guarantees the filtering error system to be mean-square asymptotically stable and has a prescribed $\cal H_{\infty}$ disturbance attenuation performance. Sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities, and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software. A numerical example is provided to illustrate the effectiveness of the proposed design method.

MSC:
93E11Filtering in stochastic control
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
93E03General theory of stochastic systems
WorldCat.org
Full Text: DOI
References:
[1] Aberkane, S.; Ponsart, J. Christophe; Sauter, D.: Output feedback H$\infty $control of a class of stochastic hybrid systems with Wiener process via convex analysis, International journal of innovative computing, information and control 6, 1179-1196 (2006)
[2] Apkarian, P.; Tuan, H. D.; Bernussou, J.: Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations, IEEE transactions on automatic control 46, 1941-1946 (2001) · Zbl 1003.93016 · doi:10.1109/9.975496
[3] Basin, M.; Perez, J.; Martinez-Zuniga, R.: Optimal filtering for nonlinear polynomial systems over linear observations with delay, International journal of innovative computing, information and control 2, 863-874 (2006)
[4] Boukas, E. K.; Yang, H.: Exponential stabilizability of stochastic systems with Markovian jumping parameters, Automatica 35, 1437-1441 (1999) · Zbl 0932.93084 · doi:10.1016/S0005-1098(99)00033-3
[5] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory, (1994) · Zbl 0816.93004
[6] Cao, Y. Y.; Lam, J.: Robust H$\infty $control of uncertain Markovian jump systems with time delay, IEEE transactions on automatic control 45, 77-83 (2000) · Zbl 0983.93075 · doi:10.1109/9.827358
[7] Du, C.; Xie, L.; Zhang, C.: H$\infty $control and robust stabilization of two-dimensional systems in roesser models, Automatica 37, 205-211 (2001) · Zbl 0970.93013 · doi:10.1016/S0005-1098(00)00155-2
[8] Gao, H.; Lam, J.; Wang, C.; Xu, S.: Robust H$\infty $filter for uncertain 2D stochastic systems, Circuits systems and signal processing 23, 479-505 (2004) · Zbl 1175.93222
[9] Gao, H.; Lam, J.; Xu, S.; Wang, C.: Stabilization and H$\infty $control of two-dimensional Markovian jump systems, IMA journal of mathematical and control information 21, 377-392 (2004) · Zbl 1069.93007 · doi:10.1093/imamci/21.4.377
[10] Hinamoto, T.: Stability of 2-D discrete systems described by the fornasini-marchesini second model, IEEE transactions on circuits and systems (I) 44, 254-257 (1997)
[11] Hoang, N. T.; Tuan, H. D.; Nguyen, T. Q.; Hosoe, S.: Robust mixed generalized H2/H$\infty $filtering of 2-D nonlinear fractional transformation systems, IEEE transactions on signal processing 53, 4697-4706 (2005)
[12] Ji, Y.; Chizeck, H. J.: Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control, IEEE transactions on automatic control 35, 777-788 (1990) · Zbl 0714.93060 · doi:10.1109/9.57016
[13] Lu, W. S.: On a Lyapunov approach to stability analysis of 2-D digital filters, IEEE transactions on circuits and systems (I) 41, 665-669 (1994)
[14] Lu, W. S.; Antoniou, A.: Two-dimensional digital filters, (1992) · Zbl 0852.93001
[15] Marszalek, W.: Two-dimensional state-space discrete models for hyperbolic partial differential equations, Applied mathematical and modeling 8, 11-14 (1984) · Zbl 0529.65039 · doi:10.1016/0307-904X(84)90170-7
[16] Shi, P.; Boukas, E. K.; Agarwal, R. K.: Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE transactions on automatic control 44, 1592-1597 (1999) · Zbl 0986.93066 · doi:10.1109/9.780431
[17] Tuan, H. D.; Apkarian, P.; Nguyen, T. Q.: Robust mixed H2/H$\infty $filtering of 2-D systems, IEEE transactions on signal processing 50, 1759-1771 (2002)
[18] Wang, Z.; Lam, J.; Liu, X. H.: Robust filtering for discrete-time Markovian jump delay systems, IEEE transactions on signal processing letters 11, 659-662 (2004)
[19] Wu, L.; Shi, P.; Gao, H.; Wang, C.: H$\infty $mode reduction for two-dimensional discrete state-delayed systems, IEE Proceedings part J: vision, image and signal processing 153, 769-784 (2006)
[20] Wu, L.; Wang, Z.; Gao, H.; Wang, C.: H$\infty $and l2-l$\infty $filtering for two-dimensional linear parametervarying systems, International journal of robust & nonlinear control 17, 1129-1154 (2007) · Zbl 1266.93153
[21] Wu, L.; Wang, Z.; Gao, H.; Wang, C.: Robust H$\infty $filtering for uncertain two-dimensional discrete systems with state delays, Signal processing 87, 2213-2230 (2007) · Zbl 1186.94370 · doi:10.1016/j.sigpro.2007.03.002
[22] Xie, L.; Ogai, H.; Inoe, Y.: Numerical solving of hybrid dynamic switching system and its application, International journal of innovative computing, information and control 2, 849-862 (2006)
[23] Xiong, J.; Lam, J.; Gao, H.; Ho, D. W. C.: On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica 41, 897-903 (2005) · Zbl 1093.93026 · doi:10.1016/j.automatica.2004.12.001
[24] Xu, S.; Chen, T.; Lam, J.: Robust H$\infty $filtering for uncertain Markovian jump systems with mode-dependent time-delays, IEEE transactions on automatic control 48, 900-907 (2003)
[25] Xu, S.; Chen, T.; Lam, J.: Robust H$\infty $filtering for a class of nonlinear discrete-time Markovian jump systems, Journal of optimization theory and applications 122, 651-668 (2004) · Zbl 1082.93056 · doi:10.1023/B:JOTA.0000042599.46775.a9
[26] Yue, D.; Fang, J.; Won, S.: Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jump parameters, Circuits, systems and signal processing 22, 351-365 (2003) · Zbl 1048.93095 · doi:10.1007/s00034-004-7036-y
[27] Zhang, H.; Basin, M.; Skliar, M.: Optimal state estimation for continuous, stochastic, state-space system with hybrid measurements, International journal of innovative computing, information and control 2, 357-370 (2006)
[28] Zhang, L.; Huang, B.; Lam, J.: H$\infty $model reduction of Markovian jump linear systems, Systems & control letters 50, 103-118 (2003) · Zbl 1157.93519 · doi:10.1016/S0167-6911(03)00133-6