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)
Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays. (English) Zbl 1254.93148
Summary: This paper considers the passivity-based control problem for stochastic jumping systems with mode-dependent round-trip time-varying delays and norm-bounded parametric uncertainties. By utilizing a novel Markovian switching Lyapunov functional, a delay-dependent passivity condition is obtained. Then, based on the derived passivity condition, a desired Markovian switching dynamic output feedback controller is designed, which ensures that the resulting closed-loop system is passive. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.
MSC:
93E03General theory of stochastic systems
93B35Sensitivity (robustness) of control systems
60J75Jump processes
References:
[1]Basin, M. V.; Rodriquez-Gonzalez, J.; Martinez-Zuniqua, R.: Optimal filtering for linear state delay systems, IEEE transactions on automatic control 50, 684-690 (2005)
[2]Basin, M. V.; Shi, P.; Calderon-Alvarez, D.: Central suboptimal H filter design for linear time-varying systems with state and measurement delay, International journal of systems science 42, 801-808 (2011)
[3]Boukas, E. K.: Stabilization of stochastic nonlinear hybrid systems, International journal of innovative computing, information and control 1, 131-141 (2005)
[4]Cao, Y. -Y.; Lam, J.; Hu, L.: Delay-dependent stochastic stability and H analysis for time-delay systems with Markovian jumping parameters, Journal of franklin institute 340, 423-434 (2003) · Zbl 1040.93068 · doi:10.1016/j.jfranklin.2003.09.001
[5]Ding, Q.; Zhong, M.: On designing H fault detection filter for Markovian jump linear systems with polytopic uncertainties, International journal of innovative computing, information and control 6, 995-1004 (2010)
[6]Fridman, E.; Shaked, U.: On delay-dependent passivity, IEEE transactions on automatic control 47, 664-669 (2002)
[7]Y. Fu, G. Duan, Stochastic stabilizability and passive control for time-delay systems with Markovian jumping parameters, in: Eighth International Conference on Control, Automation, Robotics and Vision, Kunming, China, December 2004, pp. 1757–1761.
[8]Hodgson, S.; Stoten, D. P.: Passivity-based analysis of the minimal control synthesis algorithm, International journal of control 63, 67-84 (1996) · Zbl 0854.93055 · doi:10.1080/00207179608921832
[9]Lam, J.; Gao, H.; Wang, C.: Stability analysis for continuous systems with two additive time-varying delay components, Systems control letters 56, 16-24 (2007) · Zbl 1120.93362 · doi:10.1016/j.sysconle.2006.07.005
[10]Li, H.; Gao, H.; Shi, P.: New passivity analysis for neural networks with discrete and distributed delays, IEEE transactions on neural networks 21, 1842-1847 (2010)
[11]Li, H.; Wang, C.; Shi, P.; Gao, H.: New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays, Neurocomputing 73, 3291-3299 (2010)
[12]Li, H.; Zhou, Q.; Chen, B.; Liu, H.: Parameter-dependent robust stability for uncertain Markovian jump systems with time delay, Journal of franklin institute 348, 738-748 (2011) · Zbl 1227.93126 · doi:10.1016/j.jfranklin.2011.02.002
[13]Lin, C.; Wang, Q. -G.; Lee, T. H.: A less conservative robust stability test for linear uncertain time-delay systems, IEEE transactions of automatic control 51, 87-91 (2006)
[14]Mahmoud, M. S.: Passivity and passification of jump time-delay systems, IMA journal of mathematical control information 23, 193-209 (2006) · Zbl 1095.93017 · doi:10.1093/imamci/dni053
[15]Mao, X.: Exponential stability of stochastic delay interval systems with Markovian switching, IEEE transactions on automatic control 47, 1604-1612 (2002)
[16]Nakura, G.: Stochastic optimal tracking with preview by state feedback for linear discrete-time Markovian jump systems, International journal of innovative computing, information and control 6, 15-28 (2010)
[17]Sadeghi, M. Sha; Momeni, H. R.; Amirifar, R.: H and L1 control of a teleoperation system via lmis, Applied mathematics and computation 206, 669-677 (2008) · Zbl 1152.93358 · doi:10.1016/j.amc.2008.05.051
[18]Shao, H.: Delay-range-dependent robust H filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters, Journal of mathematical analysis and applications 342, 1084-1095 (2008) · Zbl 1141.93025 · doi:10.1016/j.jmaa.2007.12.063
[19]Shen, H.; Xu, S.; Zhou, J.; Lu, J.: Fuzzy H filtering for nonlinear Markovian jump neutral systems, International journal of systems science 42, 767-780 (2011) · Zbl 1233.93091 · doi:10.1080/00207721003790351
[20]Shen, H.; Chu, Y.; Xu, S.; Zhang, Z.: Delay-dependent H control for jumping delayed systems with two Markov processes, International journal of control, automation, and systems 9, 437-441 (2011)
[21]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
[22]Wang, G.; Zhang, Q.; Sreeram, V.: H control for discrete-time singularly perturbed systems with two Markov processes, Journal of franklin institute 347, 836-847 (2010)
[23]Xia, Y.; Zhu, Z.; Mahmoud, M.: H2 control for networked control systems with Markovian data losses and delays, ICIC express letters 3, 271-276 (2009)
[24]Xu, S.; Chen, T.; Lam, J.: Robust H filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE transactions on automatic control 48, 900-907 (2003)
[25]Xu, S.; Lam, J.; Mao, X.: Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays, IEEE transactions on circuits and systems I: Regular papers 54, 2070-2077 (2007)
[26]Yin, Y.; Shi, P.; Liu, F.: Gain-scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities, Journal of franklin institute 348, 685-702 (2010) · Zbl 1227.93127 · doi:10.1016/j.jfranklin.2011.01.011
[27]Zhang, J.; Shi, P.; Qiu, J.: Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems, Journal of franklin institute 346, 676-690 (2009)