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**Stochastic optimal control and analysis of stability of networked control systems with long delay.**
*(English)*
Zbl 1175.93240

Summary: This paper generalizes well-known results to the case that network-induced delay is longer than a sampling period. The mathematical model of networked control systems whose network-induced delay is longer than a sampling period is given on this paper, when the sensor is time driven and the controller is event driven. The stochastic optimal controllers of such an networked control systems are designed. The separation theorem is proved to still hold in such networked control systems.

Reviewer: Messoud A. Efendiev (Berlin)

### MSC:

93E20 | Optimal stochastic control |

93C55 | Discrete-time control/observation systems |

93D20 | Asymptotic stability in control theory |

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\textit{S. Hu} and \textit{Q. Zhu}, Automatica 39, No. 11, 1877--1884 (2003; Zbl 1175.93240)

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### References:

[1] | Astrom, K.J., Introduction to stochastic control theory, (1970), Academic Press New York · Zbl 0387.93001 |

[2] | Beldiman, O., Walsh, G. C., & Bushnell, L. (2000). Predictors for networked control systems. Proceedings of the American control conference, Chicago, IL (pp. 2347-2351). |

[3] | Bushnell, L.G., Networks and control, IEEE control systems magazine, 21, 1, 22-23, (2001) |

[4] | Chen, H.F.; Kumar, P.R.; Schuppen, J.H.V., On Kalman filtering for conditionally Gaussian systems with random matrices, Systems & control letters, 13, 5, 397-404, (1989) · Zbl 0697.93058 |

[5] | Lian, F.L.; Moyne, J.; Tilbury, D., Performance evaluation of control networksethernet, controlnet, and devicenet, IEEE control systems magazine, 21, 1, 66-83, (2001) |

[6] | Liou, L.W.; Ray, A., A stochastic regulator for integrated communication and control systemspart Iâ€”formulation of control law, ASME journal of dynamic systems, measurement and control, 113, 4, 604-611, (1991) · Zbl 0752.93075 |

[7] | Marti, P., Villa, R., Fuertes, J. M., & Fohler, G. (2001). On real time control tasks schedulability. Proceedings of the European control conference, Porto, Portugal (pp. 2227-2232). |

[8] | Nilsson, J. (1998). Real-time control systems with delays. Ph. D. dissertation, Department of Automatic Control, Lund Institute of Technology Lund, Sweden. |

[9] | Nilsson, J.; Bernhardsson, B.; Wittenmark, B., Stochastic analysis and control of real-time systems with random time delays, Automatica, 34, 1, 57-64, (1998) · Zbl 0908.93073 |

[10] | Walsh, G.C.; Beldiman, O.; Bushnell, L.G., Asymptotic behavior of nonlinear networked control systems, IEEE transactions on automatic control, 46, 7, 1093-1097, (2001) · Zbl 1006.93040 |

[11] | Walsh, G.C.; Ye, H., Scheduling of networked control systems, IEEE control systems magazine, 21, 1, 57-65, (2001) |

[12] | Walsh, G. C., Ye, H., & Bushnell, L. G. (1999). Stability analysis of networked control systems. Proceedings of the American control conference, San Diego, CA (pp. 2876-2880). |

[13] | Yaz, E., Control of randomly varying systems with prescribed degree of stability, IEEE transactions on automatic control, 33, 4, 407-411, (1988) · Zbl 0643.93070 |

[14] | Zhang, W.; Branicky, M.S.; Philips, S.M., Stability of networked control systems, IEEE control systems magazine, 21, 1, 84-99, (2001) |

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