##
**Stabilization of networked control systems with short or long random delays: a new multirate method.**
*(English)*
Zbl 1203.93084

Summary: In this paper, the stabilization of a class of Networked Control Systems (NCSs) with time-varying delay is discussed where the random delay is less than one sensor period or more than one sensor period but bounded. A new multirate method is proposed to formulate the union model for both short and long random delays. Sufficient conditions on the existence of stabilizing controllers are established when the transition probability matrix is known. V-K iteration approach is employed to calculate the mode-dependent and mode-independent state-feedback gains of NCSs.

### MSC:

93B52 | Feedback control |

93D15 | Stabilization of systems by feedback |

93C05 | Linear systems in control theory |

93A14 | Decentralized systems |

60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |

### Keywords:

Markov chains; networked control systems; network-induced delays; multirate control; V-K iteration
PDF
BibTeX
XML
Cite

\textit{Z.-H. Guan} et al., Int. J. Robust Nonlinear Control 20, No. 16, 1802--1816 (2010; Zbl 1203.93084)

Full Text:
DOI

### References:

[1] | Lin H Zhai G Antsaklis PJ Robust stability and attenuation analysis of a class of networked control systems 1182 1187 |

[2] | Bushnell, Networks and control, IEEE Control Systems Magazine 21 (1) pp 22– (2001) |

[3] | Hu, Stochastic optimal control and analysis of stability of networked control systems with long delay, Automatica 39 (1) pp 1877– (2003) · Zbl 1175.93240 |

[4] | Walsh, Asymptotic behavior of nonlinear networked control systems, IEEE Transactions on Automatic Control 46 (7) pp 1093– (2001) · Zbl 1006.93040 |

[5] | Zhang, Stability of networked control system, IEEE Control Systems Magazine 21 (2) pp 84– (2001) |

[6] | Walsh, Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology 10 (3) pp 438– (2002) |

[7] | Nilsson, Stochastic analysis and control of real-time systems with random time delays, Automatica 34 (1) pp 57– (1998) · Zbl 0908.93073 |

[8] | Xiao L Hassibi A How JP Control with random communication delays via a discrete-time jump linear system approach 2199 2204 |

[9] | Zhu Q Lu G Cao J Hu S Stability analysis of networked control systems with Markov delay 720 724 |

[10] | Zhang, A new method for stabilization of network control systems with random delays, IEEE Transactions on Automatic Control 50 (8) pp 1177– (2005) |

[11] | Fragoso, Discrete-time Markov Jump Linear Systems (2004) |

[12] | Lian, Network design consideration for distributed control systems, IEEE Transactions on Control Systems Technology 10 (2) pp 297– (2002) |

[13] | Izadi, An opimal scheme for fast rate fault detection based on multirate sampled data, Journal of Process Control 15 pp 307– (2005) |

[14] | Hu, Stochastic stability and robust control for sampled-date systems with Markovian jump parameters, Journal of Mathematical Analysis and Applications 313 pp 504– (2006) |

[15] | Wang, Multirate sampled-data systems: computing fast-rate models, Journal of Process Control 14 pp 79– (2004) |

[16] | Izadi, An H approach to fast rate fault detection for multirate sampled-data systems, Journal of Process Control 16 pp 651– (2006) |

[17] | Georgiev, Packet-based control: the H2-optimal solution, Automatica 42 pp 137– (2006) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.