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)
Adaptive observer-based fault estimation for stochastic Markovian jumping systems. (English) Zbl 1246.93107
Summary: We study the adaptive fault estimation problems for stochastic Markovian jump systems (MJSs) with time delays. With the aid of the selected Lyapunov-Krasovskii functional, the adaptive fault estimation algorithm based on adaptive observer is proposed to enhance the rapidity and accuracy performance of fault estimation. A sufficient condition on the existence of adaptive observer is presented and proved by means of linear matrix inequalities techniques. The presented results are extended to multiple time-delayed MJSs. Simulation results illustrate that the validity of the proposed adaptive faults estimation algorithms.

MSC:
93E10Estimation and detection in stochastic control
WorldCat.org
Full Text: DOI
References:
[1] J. Gertler, “Fault detection and isolation using parity relations,” Control Engineering Practice, vol. 5, no. 5, pp. 653-661, 1997. · doi:10.1016/S0967-0661(97)00047-6
[2] H. Hammouri, M. Kinnaert, and E. H. El Yaagoubi, “Observer-based approach to fault detection and isolation for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 10, pp. 1879-1884, 1999. · Zbl 0956.93005 · doi:10.1109/9.793728
[3] S. He and F. Liu, “Fuzzy model-based fault detection for Markov jump systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 11, pp. 1248-1266, 2009. · Zbl 1166.93343 · doi:10.1002/rnc.1380
[4] S. He and F. Liu, “Filtering-based robust fault detection of fuzzy jump systems,” Fuzzy Sets and Systems, vol. 185, pp. 95-110, 2011. · Zbl 1238.93109 · doi:10.1016/j.fss.2011.05.002
[5] B. Jiang, K. Zhang, and P. Shi, “Integrated fault estimation and accommodation design for discrete-time takagiSugeno fuzzy systems with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, Article ID 5648342, pp. 291-304, 2011. · doi:10.1109/TFUZZ.2010.2095861
[6] Z. Mao, B. Jiang, and P. Shi, “Fault detection for a class of nonlinear networked control systems,” International Journal of Adaptive Control and Signal Processing, vol. 24, no. 7, pp. 610-622, 2010. · Zbl 1200.93085 · doi:10.1002/acs.1161
[7] K. Zhang, B. Jiang, and A. Shumsky, “A new criterion of fault estimation for neutral delay systems using adaptive observer,” Acta Automatica Sinica, vol. 35, no. 1, pp. 85-91, 2009. · doi:10.3724/SP.J.1004.2009.00085
[8] M. Zhong, S. X. Ding, Q.-L. Han, and Q. Ding, “Parity space-based fault estimation for linear discrete time-varying systems,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1726-1731, 2010. · doi:10.1109/TAC.2010.2046921
[9] I. A. Dzhalladova, J. Ba\vstinec, J. Diblík, and D. Y. Khusainov, “Estimates of exponential stability for solutions of stochastic control systems with delay,” Abstract and Applied Analysis, vol. 2011, Article ID 920412, 14 pages, 2011. · Zbl 1217.93150 · doi:10.1155/2011/920412
[10] J. Ba\vstinec, J. Diblík, D. Ya. Khusainov, and A. Ryvolová, “Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients,” Boundary Value Problems, vol. 2010, Article ID 956121, 20 pages, 2010. · Zbl 1214.34059 · doi:10.1155/2010/956121
[11] N. M. Krasovskii and E. A. Lidskii, “Anaytical design of controllers in systems with random attributes,” Automation and Remote Control, vol. 22, no. 1-3, pp. 1021-1025, 1141-1146, 1289-1294, 1961. · Zbl 0104.36704
[12] Z. Fei, H. Gao, and P. Shi, “New results on stabilization of Markovian jump systems with time delay,” Automatica, vol. 45, no. 10, pp. 2300-2306, 2009. · Zbl 1179.93170 · doi:10.1016/j.automatica.2009.06.020
[13] N. S. D. Arrifano and V. A. Oliveira, “Robust H\infty fuzzy control approach for a class of Markovian jump nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 6, pp. 738-754, 2006. · doi:10.1109/TFUZZ.2006.877359
[14] Z. Xiang, R. Wang, and Q. Chen, “Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7725-7736, 2011. · Zbl 1232.93093 · doi:10.1016/j.amc.2011.02.076
[15] S. He and F. Liu, “Robust finite-time stabilization of uncertain fuzzy jump systems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 9, pp. 3853-3862, 2010.
[16] Q. Ding and M. Zhong, “On designing H\infty fault detection filter for Markovian jump linear systems with polytopic uncertainties,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 3, pp. 995-1004, 2010.
[17] Z. Mao, B. Jiang, and P. Shi, “Fault detection for a class of nonlinear networked control systems,” International Journal of Adaptive Control and Signal Processing, vol. 24, no. 7, pp. 610-622, 2010. · Zbl 1200.93085 · doi:10.1002/acs.1161
[18] N. Meskin and K. Khorasani, “Fault Detection and Isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels,” Automatica, vol. 45, no. 9, pp. 2032-2040, 2009. · Zbl 1175.93142 · doi:10.1016/j.automatica.2009.04.020
[19] Z. Ding, “Adaptive estimation and rejection of unknown sinusoidal disturbances in a class of non-minimum-phase nonlinear systems,” IEE Proceedings-Control Theory and Applications, vol. 153, no. 4, pp. 379-386, 2006. · doi:10.1049/ip-cta:20045283
[20] G. Feng, S. G. Cao, and N. W. Rees, “Stable adaptive control for fuzzy dynamic systems,” Fuzzy Sets and Systems, vol. 131, no. 2, pp. 217-224, 2002. · Zbl 1010.93517 · doi:10.1016/S0165-0114(01)00236-6
[21] H. Wang and S. Daley, “Actuator fault diagnosis: an adaptive observer-based technique,” IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 1073-1078, 1996. · Zbl 0858.93040 · doi:10.1109/9.508919
[22] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[23] X. Mao, “Stability of stochastic differential equations with Markovian switching,” Stochastic Processes and Their Applications, vol. 79, no. 1, pp. 45-67, 1999. · Zbl 0962.60043 · doi:10.1016/S0304-4149(98)00070-2
[24] M. Grant, S. Boyd, and Y. Ye, “Disciplined convex programming,” in Global Optimization, vol. 84 of Nonconvex Optimization and Its Applications, pp. 155-210, Springer, New York, NY, USA, 2006. · Zbl 1130.90382 · doi:10.1007/0-387-30528-9_7