Stability analysis for networked control systems based on average dwell time method.

*(English)*Zbl 1204.93052Summary: This paper studies the problem of the exponential stability of Networked Control Systems (NCSs) with large delay periods, which often appear in the transmission of NCSs. Some new concepts about large delay periods are introduced, and a method based on switching is employed. The maximum allowable transfer interval is obtained such that the considered system is exponentially stable. The criteria obtained contain existing results without considering a large delay period as a special case. An example is given to show the effectiveness of the proposed criteria.

##### MSC:

93B52 | Feedback control |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D30 | Lyapunov and storage functions |

93C15 | Control/observation systems governed by ordinary differential equations |

##### Keywords:

networked control systems; average dwell time method; switched delay systems; piecewise Lyapunov functional
PDF
BibTeX
XML
Cite

\textit{X.-M. Sun} et al., Int. J. Robust Nonlinear Control 20, No. 15, 1774--1784 (2010; Zbl 1204.93052)

Full Text:
DOI

##### References:

[1] | Seiler, An H approach to networked control, IEEE Transaction on Automatic Control 50 (3) pp 356– (2005) · Zbl 1365.93147 |

[2] | Tang, Feedback scheduling of model-based networked control systems with flexible workload, International Journal of Automation and Computing 5 (4) pp 389– (2008) |

[3] | Ren, Linearizing control of induction motor based on networked control systems, International Journal of Automation and Computing 6 (2) pp 192– (2009) |

[4] | Liu, Design and stability criteria of networked predictive control systems with random network delay in the feedback channel, IEEE Transactions on Systems, Man and Cybernetics 37 (2) pp 173– (2007) |

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

[6] | Xie, Stabilization of networked control systems with time-varying network-induced delay, Forty-third IEEE Conference on Decision and Control 4 pp 3551– (2004) |

[7] | Montestruque, Stability of model-based networked control systems with time-varying transmission times, IEEE Transactions on Automatic Control 49 pp 1562– (2004) · Zbl 1365.90039 |

[8] | Zhang, Stability of networked control systems, IEEE Control Systems Magazine 21 (1) pp 84– (2001) |

[9] | Park, A scheduling method for network based control systems, IEEE Transactions on Control Systems Technology 10 pp 318– (2002) |

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

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

[12] | Kim, Maximum allowable delay bounds of networked control systems, Control Engineering Practice 11 pp 1301– (2003) |

[13] | Yue, State feedback controller design of networked control systems, IEEE Transactions on Circuits and Systems II: Express Briefs 51 (11) pp 640– (2004) |

[14] | Yue, Network-based robust H control of systems with uncertainty, Automatica 41 pp 999– (2005) |

[15] | Hale, Applied Mathematical Sciences, in: Introduction to Functional Differential Equations (1993) · doi:10.1007/978-1-4612-4342-7 |

[16] | Gu, Stability of Time-delay Systems (2003) · Zbl 1039.34067 · doi:10.1007/978-1-4612-0039-0 |

[17] | Fridman, An improved stabilization method for linear time-delay systems, IEEE Transactions on Automatic Control 47 (11) pp 1931– (2002) |

[18] | Gao, Comments and further results on ’A descriptor system approach to H control of linear time-delay systems’, IEEE Transactions on Automatic Control 48 (3) pp 520– (2003) |

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

[20] | Basin, Optimal linear filtering for systems with multiple state and observation delays, International Journal of Innovative Computing, Information and Control 3 (5) pp 1309– (2007) |

[21] | Han, On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica 40 (6) pp 1087– (2004) · Zbl 1073.93043 |

[22] | Hespanha JP Morse AS Stability of switched systems with average dwell-time 2655 2660 |

[23] | Liberzon, Switching in Systems and Control (2003) · doi:10.1007/978-1-4612-0017-8 |

[24] | Zhai, Disturbance attenuation properties of time-controlled switched systems, Journal of the Franklin Institute 338 pp 765– (2001) · Zbl 1022.93017 |

[25] | Zhai, Controller failure time analysis for symmetric H control, International Journal of Control 77 (6) pp 598– (2004) · Zbl 1059.93040 |

[26] | He, Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE Transactions on Automatic Control 49 (5) pp 828– (2004) · Zbl 1365.93368 |

[27] | He, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and Control Letters 51 (1) pp 57– (2004) · Zbl 1157.93467 |

[28] | Sun, Stability and L2-gain analysis for switched delay systems: a delay-dependent method, Automatica 42 (10) pp 1769– (2006) |

[29] | Xu, On equivalence and efficiency of certain stability criteria for time-delay systems, IEEE Transactions on Automatic Control 52 (1) pp 95– (2007) · Zbl 1366.93451 |

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.