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Introduction

  • Chapter
Nonlinear Stochastic Systems with Incomplete Information

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Abstract

In Chap. 1, the research background on the filtering and control problems for nonlinear stochastic complex systems with incomplete information is introduced. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are comprehensive that include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Finally, the outline of the book is listed.

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References

  1. Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice-Hall, Englewood Cliffs (1979)

    MATH  Google Scholar 

  2. Ball, J.A., Helton, J.W., Walker, M.L.: H ∞ control for nonlinear systems with output feedback. IEEE Trans. Autom. Control 38(4), 546–559 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(15), 509–512 (1999)

    MathSciNet  Google Scholar 

  4. Basin, M., Sanchez, E., Martinez-Zuniga, R.: Optimal filtering for linear systems over polynomial observations. Int. J. Innov. Comput. Inf. Control 4(2), 313–320 (2008)

    Google Scholar 

  5. Basin, M., Sanchez, E., Martinez-Zuniga, R.: Optimal linear filtering for systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 3(5), 1309–1320 (2008)

    Google Scholar 

  6. Berman, N., Shaked, U.: H ∞ control for discrete-time nonlinear stochastic systems. IEEE Trans. Autom. Control 51(6), 1041–1046 (2006)

    Article  MathSciNet  Google Scholar 

  7. Berman, N., Shaked, U.: H ∞-like control for nonlinear stochastic systems. Syst. Control Lett. 55(3), 247–257 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bliman, P.A., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. Automatica 44(8), 1985–1995 (2008)

    Article  MathSciNet  Google Scholar 

  9. Boukas, E.K., Liu, Z.-K.: Deterministic and Stochastic Time-Delay Systems. Birkhäuser, Boston (2002)

    Book  MATH  Google Scholar 

  10. Brockett, R., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Trans. Autom. Control 45(7), 1279–1289 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Buhmann, J., Schulten, K.: Influence of noise on the function of a ‘physiological’ neural network. Biol. Cybern. 56(5–6), 313–327 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16(1) (2006). Art. no. 013133, doi:10.1063/1.2178448

  13. Cao, Y., Lin, Z., Chen, B.: An output feedback H ∞ controller design for linear systems subject to sensor nonlinearities. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50(7), 914–921 (2003)

    Article  MathSciNet  Google Scholar 

  14. Cao, Y., Lin, Z., Ward, D.: An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation. IEEE Trans. Autom. Control 47(1), 140–145 (2002)

    Article  MathSciNet  Google Scholar 

  15. Cao, Y., Lin, Z., Ward, D.: H ∞ antiwindup design for linear systems subject to input saturation. J. Guid. Control Dyn. 25(3), 455–463 (2002)

    Article  Google Scholar 

  16. Cattivelli, F.S., Lopes, C.G., Sayed, A.H.: Diffusion strategies for distributed Kalman filtering: formulation and performance analysis. In: Proc. Cognitive Information Processing, Santorini, Greece (2008)

    Google Scholar 

  17. Cattivelli, F.S., Sayed, A.H.: Diffusion mechanisms for fixed-point distributed Kalman smoothing. In: Proc. EUSIPCO, Lausanne, Switzerland (2008)

    Google Scholar 

  18. Charalambous, C.D.: Stochastic nonlinear minimax dynamic games with noisy measurements. IEEE Trans. Autom. Control 48(2), 261–266 (2003)

    Article  MathSciNet  Google Scholar 

  19. Chen, T., Francis, B.A.: Linear time-varying H 2-optimal control of sampled-data systems. Automatica 27(6), 963–974 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Chen, T., Qiu, L.: H ∞ design of general multirate sampled-data control-systems. Automatica 30(7), 1139–1152 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  21. Cimatti, G., Rovatti, R., Setti, G.: Chaos-based spreading in DS-UWB sensor networks increases available bit rate. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(6), 1327–1339 (2007)

    Article  MathSciNet  Google Scholar 

  22. Delchumps, D.F.: Stabilizing a linear system with quantized state feedback. IEEE Trans. Autom. Control 35(8), 916–924 (1990)

    Article  Google Scholar 

  23. Delvenne, J.C.: An optimal quantized feedback strategy for scalar linear systems. IEEE Trans. Autom. Control 51(2), 298–303 (2006)

    Article  MathSciNet  Google Scholar 

  24. Deng, H., Krstic, M.: Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance. Syst. Control Lett. 39, 173–182 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  25. Deng, H., Krstic, M., Williams, R.: Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Trans. Autom. Control 46, 1237–1253 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  26. Du, C., Xie, L., Soh, Y.C.: H ∞ reduced-order approximation of 2-D digital filters. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(6), 688–698 (2001)

    Article  MATH  Google Scholar 

  27. Duan, Z., Chen, G., Huang, L.: Disconnected synchronized regions of complex dynamical networks. IEEE Trans. Autom. Control 54(4), 845–849 (2009)

    Article  MathSciNet  Google Scholar 

  28. Elia, N., Mitter, K.: Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. Fei, Z., Gao, H., Zheng, W.: New synchronization stability of complex networks with an interval time-varying coupling delay. IEEE Trans. Circuits Syst. II, Express Briefs 56(6), 499–503 (2009)

    Article  Google Scholar 

  30. Fridman, E., Dambrine, M.: Control under quantization, saturation and delay: an LMI approach. Automatica 45(10), 2258–2264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Fridman, E., Seuret, A., Richard, J.P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1441–1446 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Fridman, E., Shaked, U., Suplin, V.: Input/output delay approach to robust sampled-data H ∞ control. Syst. Control Lett. 54(3), 271–282 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  33. Fu, M., Xie, L.: The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1689–1711 (2005)

    MathSciNet  Google Scholar 

  34. Gelb, A.: Applied Optimal Estimation. Cambridge University Press, Cambridge (1974)

    Google Scholar 

  35. Gao, H., Chen, T.: H ∞ estimation for uncertain systems with limited communication capacity. IEEE Trans. Autom. Control 52(11), 2070–2084 (2007)

    Article  MathSciNet  Google Scholar 

  36. Gao, H., Chen, T., Chai, T.: Passivity and pacification for networked control systems. SIAM J. Control Optim. 46(4), 1299–1322 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  37. Gao, H., Lam, J., Chen, G.: New criteria for synchronization stability of general complex dynamical networks with coupling delays. Phys. Lett. A 360(2), 263–273 (2006)

    Article  MATH  Google Scholar 

  38. Gao, H., Meng, X., Chen, T.: H ∞ filter design for discrete delay systems: a new parameter-dependent approach. Int. J. Control 82(6), 993–1005 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Gao, H., Wu, J., Shi, P.: Robust sampled-data H ∞ control with stochastic sampling. Automatica 45(7), 1729–1736 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gao, H., Zhao, Y., Lam, J., Chen, K.: H ∞ fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Trans. Fuzzy Syst. 17(2), 291–300 (2009)

    Article  Google Scholar 

  41. He, W., Cao, J.: Exponential synchronization of hybrid coupled networks with delayed coupling. IEEE Trans. Neural Netw. 21(4), 571–583 (2010)

    Article  Google Scholar 

  42. He, X., Wang, Z., Zhou, D.: Robust H ∞ filtering for networked systems with multiple state delays. Int. J. Control 80(8), 1217–1232 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  43. He, Y., Wang, Q., Wu, M., Lin, C.: Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Netw. 17(4), 1077–1081 (2006)

    Article  MATH  Google Scholar 

  44. Hou, Z., Cheng, L., Tan, M.: Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39(3), 636–647 (2009)

    Article  Google Scholar 

  45. Hu, T., Lin, Z., Chen, B.: Analysis and design for discrete-time linear systems subject to actuator saturation. Syst. Control Lett. 45(2), 97–112 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  46. Hu, X., Wang, J.: Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 37(5), 1414–1421 (2007)

    Article  Google Scholar 

  47. Jost, J., Joy, M.: Spectral properties and synchronization in coupled map lattices. Phys. Rev. E 65(4), 1025–1032 (2002). Art. no. 061201

    MathSciNet  Google Scholar 

  48. Karimi, H.R., Gao, H.: New delay-dependent exponential H ∞ synchronization for uncertain neural networks with mixed time delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(1), 173–185 (2010)

    Article  Google Scholar 

  49. Li, H., Yue, D.: Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays. J. Phys. A, Math. Theoret. 43(10) (2010). Art. no. 105101, doi:10.1088/1751-8113/43/10/105101

  50. Li, P., Lam, J., Shu, Z.: On the transient and steady-state estimates of interval genetic regulatory networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(2), 336–349 (2010)

    Article  Google Scholar 

  51. Li, T., Zhang, J.: Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica 45(8), 1929–1936 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  52. Li, Z., Chen, G.: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuits Syst. II, Express Briefs 53(1), 28–33 (2006)

    Article  Google Scholar 

  53. Li, Z., Duan, Z., Chen, G., Huang, L.: Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circuits Syst. I, Regul. Pap. 57(1), 213–224 (2010)

    Article  MathSciNet  Google Scholar 

  54. Liang, J., Wang, Z., Liu, Y., Liu, X.: Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Trans. Neural Netw. 19(11), 1910–1921 (2008)

    Article  Google Scholar 

  55. Liberzon, D.: Hybrid feedback stabilization of systems with quantized signals. Automatica 39(9), 1543–1554 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  56. Lin, P., Jia, Y., Li, L.: Distributed robust H ∞ consensus control in directed networks of agents with time-delay. Syst. Control Lett. 57(8), 643–653 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  57. Liu, Y., Pan, Z., Shi, S.: Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE Trans. Autom. Control 48(3), 509–513 (2003)

    Article  MathSciNet  Google Scholar 

  58. Liu, Y., Wang, Z., Liang, J., Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38(5), 1314–1325 (2008)

    Article  MathSciNet  Google Scholar 

  59. Liu, Y., Wang, Z., Liu, X.: Design of exponential state estimators for neural networks with mixed time decays. Phys. Lett. A 364, 401–412 (2007)

    Article  Google Scholar 

  60. Lu, B., Gungor, V.C.: Online and remote motor energy monitoring and fault diagnostics using wireless sensor networks. IEEE Trans. Ind. Electron. 56(11), 4651–4659 (2009)

    Article  Google Scholar 

  61. Lü, J., Chen, G.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control 50(6), 841–846 (2005)

    Article  Google Scholar 

  62. Lu, W., Chen, T.: Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits Syst. I, Regul. Pap. 51(12), 2491–2503 (2004)

    Article  MathSciNet  Google Scholar 

  63. Lu, W., Chen, T.: Global synchronization of discrete-time dynamical network with a directed graph. IEEE Trans. Circuits Syst. II, Express Briefs 54(2), 136–140 (2007)

    Article  Google Scholar 

  64. Lu, X., Xie, L., Zhang, H., Wang, W.: Robust Kalman filtering for discrete-time systems with measurement delay. IEEE Trans. Circuits Syst. II, Express Briefs 54(6), 522–526 (2007)

    Article  Google Scholar 

  65. Mahmoud, M., Shi, Y., Nounou, H.: Resilient observer-based control of uncertain time-delay systems. Int. J. Innov. Comput. Inf. Control 3(2), 407–418 (2007)

    Google Scholar 

  66. McEneaney, W.M., Yin, G., Zhang, Q. (eds.): Stochastic Analysis, Control, Optimization and Applications. Systems and Control: Foundations and Applications Series. Birkhäuser, Boston (1999)

    MATH  Google Scholar 

  67. Mou, S., Gao, H., Lam, J., Qiang, W.: A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 19(3), 532–535 (2008)

    Article  Google Scholar 

  68. Nguang, S.K., Shi, P.: Nonlinear H ∞ filtering of sampled-data systems. Automatica 36(2), 303–310 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  69. Nguang, S.K., Shi, P.: H ∞ filtering design for uncertain nonlinear systems under sampled measurements. Int. J. Syst. Sci. 32(7), 889–898 (2001)

    MathSciNet  MATH  Google Scholar 

  70. Olfati-Saber, R.: Distributed Kalman filtering for sensor networks. In: Proc. 46th IEEE Conference Decision and Control, New Orleans, LA (2007)

    Google Scholar 

  71. Olfati-Saber, R., Murray, R.M.: Consensus problems in the networks of agents with switching topology and time delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  72. Olfati-Saber, R., Shamma, J.: Consensus filters for sensor networks and distributed sensor fusion. In: 44th IEEE Conference on Decision and Control, 2005; and 2005 European Control Conference, CDC-ECC’05, pp. 6698–6703. IEEE, New York (2005)

    Google Scholar 

  73. Palm, R.: Synchronization of decentralized multiple-model systems by market-based optimization. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 34(1), 665–672 (2004)

    Article  MathSciNet  Google Scholar 

  74. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  75. Peng, C., Tian, Y.: Networked H ∞ control of linear systems with state quantization. Inf. Sci. 177(24), 5763–5774 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  76. Perez-Munuzuri, V., Perez-Villar, V., Chua, L.O.: Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 40(3), 174–181 (1993)

    Article  MATH  Google Scholar 

  77. Qiu, L., Chen, T.: H 2-optimal design of multirate sampled-data systems. IEEE Trans. Autom. Control 39(12), 2506–2511 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  78. Qiu, L., Chen, T.: Multirate sampled-data systems: all H ∞ suboptimal controllers and the minimum entropy controller. IEEE Trans. Autom. Control 44(3), 537–550 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  79. Sahebsara, M., Chen, T., Shah, S.L.: Optimal H 2 filtering in networked control systems with multiple packet dropout. IEEE Trans. Autom. Control 52(8), 1508–1513 (2007)

    Article  MathSciNet  Google Scholar 

  80. Sahebsara, M., Chen, T., Shah, S.L.: Optimal H ∞ filtering in networked control systems with multiple packet dropouts. Syst. Control Lett. 57(9), 696–702 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  81. der Schaft, A.J.V.: l 2-gain analysis of nonlinear systems and nonlinear state feedback H ∞ control. IEEE Trans. Autom. Control 37(6), 770–784 (1992)

    Article  MATH  Google Scholar 

  82. Schizas, I., Roumeliotis, S.I., Giannakis, G.B., Ribeiro, A.: Anytime optimal distributed Kalman filtering and smoothing. In: Proc. IEEE Workshop on Statistical Signal Process, Madison, WI (2007)

    Google Scholar 

  83. Shaked, U., Berman, N.: H ∞ nonlinear filtering of discrete-time processes. IEEE Trans. Signal Process. 43(9), 2205–2209 (1995)

    Article  Google Scholar 

  84. Shi, G., Hong, Y.: Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica 45(5), 1165–1175 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  85. Shi, P.: Filtering on sampled-data systems with parametric uncertainty. IEEE Trans. Autom. Control 43(7), 1022–1027 (1998)

    Article  MATH  Google Scholar 

  86. Shi, P., Mahmoud, M., Nguang, S.K., Ismail, A.: Robust filtering for jumping systems with mode-dependent delays. Signal Process. 43(7), 1022–1027 (2006)

    Google Scholar 

  87. Shu, Z., Lam, J.: Global exponential estimates of stochastic interval neural networks with discrete and distributed delays. Neurocomputing 71(13–15), 2950–2963 (2008)

    Article  Google Scholar 

  88. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M.I., Sastry, S.S.: Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49(9), 1453–1464 (2004)

    Article  MathSciNet  Google Scholar 

  89. Souza, F., Palhares, R.: Synchronisation of chaotic delayed artificial neural networks: an H ∞ control approach. Int. J. Syst. Sci. 40(9), 937–944 (2009)

    Article  MathSciNet  Google Scholar 

  90. Speranzon, A., Fischione, C., Johansson, K.H., Sangiovanni-Vincentelli, A.: A distributed minimum variance estimator for sensor networks. IEEE J. Sel. Areas Commun. 26(4), 609–621 (2008)

    Article  Google Scholar 

  91. Stanković, S.S., Stanković, M.S., Stipanović, D.M.: Consensus based overlapping decentralized estimation with missing observations and communication faults. Automatica 45(6), 1397–1406 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  92. Sun, S., Xie, L., Xiao, W.: Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts. IEEE Trans. Signal Process. 56(8), 4031–4038 (2008)

    Article  MathSciNet  Google Scholar 

  93. Sun, Y., Wang, L., Xie, G.: Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. Syst. Control Lett. 57(2), 175–183 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  94. Tian, E., Yue, D., Peng, C.: Quantized output feedback control for networked control systems. Inf. Sci. 178(12), 2734–2749 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  95. Toroczkai, Z.: Complex networks: the challenge of interaction topology. Los Alamos Sci. 29, 94–109 (2005)

    Google Scholar 

  96. Wang, X., Chen, G.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos 12(1), 187–192 (2002)

    Article  Google Scholar 

  97. Wang, Z., Ho, D.W.C., Liu, X.: Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Trans. Autom. Control 48(7), 1254–1258 (2003)

    Article  MathSciNet  Google Scholar 

  98. Wang, Z., Ho, D.W.C., Liu, X.: Robust filtering under randomly varying sensor delay with variance constraints. IEEE Trans. Circuits Syst. II, Express Briefs 51(6), 320–326 (2004)

    Article  Google Scholar 

  99. Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16(1), 279–284 (2005)

    Article  Google Scholar 

  100. Wang, Z., Ho, D.W.C., Liu, Y., Liu, X.: Robust H ∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. Automatica 45(3), 684–691 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  101. Wang, Z., Huang, B., Huo, P.: Sampled-data filtering with error covariance assignment. IEEE Trans. Signal Process. 49(3), 666–670 (2001)

    Article  Google Scholar 

  102. Wang, Z., Liu, Y., Liu, X.: H ∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. Automatica 44(5), 1268–1277 (2008)

    Article  MathSciNet  Google Scholar 

  103. Wang, Z., Yang, F., Ho, D.W.C., Liu, X.: Robust H ∞ filtering for stochastic time-delay systems with missing measurements. IEEE Trans. Signal Process. 54(7), 2579–2587 (2006)

    Article  Google Scholar 

  104. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  105. Wei, G., Shu, H.: H ∞ filtering on nonlinear stochastic systems with delay. Chaos Solitons Fractals 33(2), 663–670 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  106. Wei, G., Wang, Z., Shu, H.: Robust filtering with stochastic nonlinearities and multiple missing measurements. Automatica 45(3), 836–841 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  107. Wood, K., den Broeck, C.V., Kawai, R., Lindenberg, K.: Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators. Phys. Rev. E 76(4) (2007). Art. no. 041132, doi:10.1103/PhysRevE.76.041132

  108. Wu, J., Chen, X., Gao, H.: H ∞ filtering with stochastic sampling. Signal Process. 90(4), 1131–1145 (2010)

    Article  MATH  Google Scholar 

  109. Wu, L., Shi, P., Gao, H., Wang, C.: H ∞ filtering for 2D Markovian jump systems. Automatica 44(7), 1849–1858 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  110. Xiao, F., Wang, L.: Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica 44(10), 2577–2582 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  111. Xiao, L., Boyed, S.: Fast linear iterations for distributed averaging. Syst. Control Lett. 53(1), 65–78 (2004)

    Article  MATH  Google Scholar 

  112. Xiao, Y., Cao, Y., Lin, Z.: Robust filtering for discrete-time systems with saturation and its application to transmultiplexers. IEEE Trans. Signal Process. 52(2), 1266–1277 (2004)

    Article  MathSciNet  Google Scholar 

  113. Xie, S., Xie, L.: Decentralized stabilization of a class of interconnected stochastic nonlinear systems. IEEE Trans. Autom. Control 45(1), 132–137 (2000)

    Article  MATH  Google Scholar 

  114. Xu, S., Lam, J.: A survey of linear matrix inequality techniques in stability analysis of delay systems. Int. J. Syst. Sci. 39(12), 1095–1113 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  115. Xu, S., Lam, J., Mao, X.: Delay-dependent H ∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(9), 2070–2077 (2007)

    Article  MathSciNet  Google Scholar 

  116. Yang, F., Li, Y.: Set-membership filtering for systems with sensor saturation. Automatica 45(8), 1896–1902 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  117. Yang, F., Wang, Z., Feng, G., Liu, X.: Robust filtering with randomly varying sensor delay: the finite-horizon case. IEEE Trans. Circuits Syst. I, Regul. Pap. 56(3), 1310–1314 (2009)

    MathSciNet  Google Scholar 

  118. Yang, F., Wang, Z., Hung, Y.S.: Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises. IEEE Trans. Autom. Control 47(7), 1179–1183 (2002)

    Article  MathSciNet  Google Scholar 

  119. Yaz, E., Ray, A.: Linear unbiased state estimation for random models with sensor delay. In: Proc. Conf. on Decision & Control, Kobe, Japan, pp. 47–52 (1996)

    Google Scholar 

  120. Yu, W., Chen, G., Wang, Z., Yang, W.: Distributed consensus filtering in sensor networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39(6), 1568–1577 (2009)

    Article  Google Scholar 

  121. Yue, D., Peng, C., Tang, G.Y.: Guaranteed cost control of linear systems over networks with state and input quantisations. IEE Proc., Control Theory Appl. 153(6), 658–664 (2006)

    Article  MathSciNet  Google Scholar 

  122. Zhang, W., Chen, B.S., Tseng, C.S.: Robust H ∞ filtering for nonlinear stochastic systems. IEEE Trans. Signal Process. 53(2), 589–598 (2005)

    Article  MathSciNet  Google Scholar 

  123. Zhong, W., Stefanovski, J.D., Dimirovski, G.M., Zhao, J.: Decentralized control and synchronization of time-varying complex dynamical network. Kybernetika 45(1), 151–167 (2009)

    MathSciNet  MATH  Google Scholar 

  124. Zhou, S., Feng, G.: H ∞ filtering for discrete-time systems with randomly varying sensor delays. Automatica 44(7), 1918–1922 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  125. Zuo, Z., Ho, D.W.C., Wang, Y.: Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation. Automatica 46(3), 569–576 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  126. Zuo, Z., Wang, J., Huang, L.: Output feedback H ∞ controller design for linear discrete-time systems with sensor nonlinearities. IEE Proc., Control Theory Appl. 152(1), 9–26 (2005)

    Article  Google Scholar 

  127. Zuo, Z., Yang, C., Wang, Y.: A unified framework of exponential synchronization for complex networks with time-varying delays. Phys. Lett. A 374(19–20), 1989–1999 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Inform. Science & Technol., Donghua University, Shanghai, China, People’s Republic

    Bo Shen & Huisheng Shu

  2. Dept. of Information Systems & Computing, Brunel University, Uxbridge, UK

    Zidong Wang

Authors
  1. Bo Shen
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  2. Zidong Wang
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  3. Huisheng Shu
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Shen, B., Wang, Z., Shu, H. (2013). Introduction. In: Nonlinear Stochastic Systems with Incomplete Information. Springer, London. https://doi.org/10.1007/978-1-4471-4914-9_1

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  • DOI: https://doi.org/10.1007/978-1-4471-4914-9_1

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