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**Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays.**
*(English)*
Zbl 1261.93076

Summary: In this paper, the distributed state estimation problem is investigated for a class of sensor networks described by uncertain discrete-time dynamical systems with Markovian jumping parameters and distributed time-delays. The sensor network consists of sensor nodes characterized by a directed graph with a nonnegative adjacency matrix that specifies the interconnection topology (or the distribution in the space) of the network. Both the parameters of the target plant and the sensor measurements are subject to the switches from one mode to another at different times according to a Markov chain. The parameter uncertainties are norm-bounded that enter into both the plant system as well as the network outputs. Furthermore, the distributed time-delays are considered, which are also dependent on the Markovian jumping mode. Through the measurements from a small fraction of the sensors, this paper aims to design state estimators that allow the nodes of the sensor network to track the states of the plant in a distributed way. It is verified that such state estimators do exist if a set of matrix inequalities is solvable. A numerical example is provided to demonstrate the effectiveness of the designed distributed state estimators.

### MSC:

93E10 | Estimation and detection in stochastic control theory |

93C55 | Discrete-time control/observation systems |

60J75 | Jump processes (MSC2010) |

### Keywords:

distributed state estimation; sensor network; parameter uncertainties; Markovian chain; mode-dependent distributed delays
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\textit{J. Liang} et al., Int. J. Robust Nonlinear Control 22, No. 3, 331--346 (2012; Zbl 1261.93076)

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### References:

[1] | Brooks, Distributed target classification and tracking in sensor networks, Proceedings of the IEEE 91 (8) pp 1163– (2003) |

[2] | Xiong, Distributed source coding for sensor networks, IEEE Signal Processing Magazine pp 80– (2004) |

[3] | Liu, Design of reduced-order filter for Markovian jumping systems with time delay, IEEE Transactions on Circuits and Systems-II 51 (11) pp 1837– (2006) |

[4] | Gao, H estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control 52 (11) pp 2070– (2007) · Zbl 1366.93155 |

[5] | Shi, Robust filtering for jumping systems with mode-dependent delays, Signal Processing 86 (1) pp 140– (2006) · Zbl 1163.94387 |

[6] | Wu, filtering for 2D Markovian jump systems, Automatica 44 (7) pp 1849– (2008) · Zbl 1149.93346 |

[7] | Xiong, Fixed-order robust filter design for Markovian jump systems with uncertain switching probabilities, IEEE Transactions on Signal Processing 54 (4) pp 1421– (2006) · Zbl 1373.94736 |

[8] | Zhang, filtering for multiple-time-delay measurements, IEEE Transactions on Signal Processing 54 (5) pp 1681– (2006) · Zbl 1373.94749 |

[9] | Chai L Hu B Jiang P Distributed state estimation based on quantized observations in a bandwidth constrained sensor network 2411 2415 |

[10] | Olfati-Saber R Distributed Kalman filtering for sensor networks |

[11] | Olfati-Saber R Shamma JS Consensus filters for sensor networks and distributed sensor fusion · Zbl 1112.68470 |

[12] | Speranzon, A distributed minimum variance estimator for sensor networks, IEEE Journal on Selected Areas in Communications 26 (4) pp 609– (2008) |

[13] | Kim JH West M Scholte E Narayanan S Multiscale consensus for decentralized estimation and its application to building systems 888 893 |

[14] | Yu, Distributed consensus filtering in sensor networks, IEEE Transactions on Systems, Man, and Cybernetics-B 39 (6) pp 1568– (2009) |

[15] | Cattivelli, Diffusion LMS strategies for distributed estimation, IEEE Transactions on Signal Processing 58 (3) pp 1035– (2010) · Zbl 1368.93706 |

[16] | Cattivelli, Diffusion strategies for distributed Kalman filtering and smoothing, IEEE Transactions on Automatic Control (2010) · Zbl 1368.93706 |

[17] | Chen, Jumping ant routing algorithm for sensor networks, Computer Communications 30 pp 2892– (2007) · Zbl 05397944 |

[18] | Gunawan, Reliability analysis of shuffle-exchange network systems, Reliability Engineering and System Safety 93 pp 271– (2008) |

[19] | Liu, Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Transactions on Systems, Man, and Cybernetics 38 (5) pp 1314– (2008) |

[20] | Patan M Ucinski D Conguration of sensor network with uncertain location of nodes for parameter estimation in distributed parameter systems 2009 |

[21] | Busch, Efficient bufferless packet switching on trees and leveled networks, Journal of Parallel and Distributed Computing 67 (11) pp 1168– (2007) · Zbl 1125.68005 |

[22] | Boukas, Robust H control of discrete-time Markovian jump linear systems with mode-dependent time-delays, IEEE Transactions on Automatic Control 46 pp 1918– (2001) · Zbl 1005.93050 |

[23] | Liu, State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays, Physics Letters A 372 pp 7147– (2008) · Zbl 1227.92002 |

[24] | Liu, Exponential synchronization of complex networks with Markovian jump and mixed delays, Physics Letters A 372 pp 3986– (2008) · Zbl 1220.90040 |

[25] | Liu, Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays, IEEE Transactions on Neural Networks 20 (7) pp 1102– (2009) · Zbl 1165.90365 |

[26] | Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 |

[27] | Zhao, Stability and atabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE Transactions on Fuzzy Systems 17 (4) pp 750– (2009) |

[28] | Zhao, H control of nonlinear dynamic systems: a new fuzzy delay fractioning approach, IET Control Theory and Applications 3 (7) pp 917– (2009) |

[29] | Martin, Optimal tuning of a networked linear controller using a multi-objective genetic algorithm and its application to one complex electromechanical process, International Journal of Innovative Computing, Information and Control 5 (10(B)) pp 3405– (2009) |

[30] | Vesely, Robust output networked control system design, ICIC Express Letters 4 (4) pp 1399– (2010) |

[31] | Xia, H2 control for networked control systems with Markovian data losses and delays, ICIC Express Letters 3 (3(A)) pp 271– (2009) |

[32] | Zhu, State feedback controller design of networked control systems with time delay in the plant, International Journal of Innovative Computing, Information and Control 4 (2) pp 283– (2008) |

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