Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections.

*(English)*Zbl 1158.93306Summary: The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking error between each time-delay subsystem and the corresponding local reference model without time-delay decreases uniformly asymptotically to zero. In this paper, it is assumed that the time-varying delays are any continuous and bounded nonnegative functions, and the proposed decentralized robust tracking controllers are independent of the delays. Therefore, the results obtained in the paper are applicable to large scale systems without exact knowledge of the delays, i.e. large systems with perturbed delays.

##### MSC:

93A14 | Decentralized systems |

93A15 | Large-scale systems |

93B52 | Feedback control |

93D21 | Adaptive or robust stabilization |

34K06 | Linear functional-differential equations |

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##### References:

[1] | B. Brogliato and A. Trofino Neto: Practical stabilization of a class of nonlinear systems with partially known uncertainties. Automatica 31 (1995), 145-150. · Zbl 0825.93650 |

[2] | C. H. Choi and H. S. Kim: Adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds. IEEE Trans. Automat. Control 38 (1993), 1246-1250. · Zbl 0784.93053 |

[3] | S. Gutman: Uncertain dynamical systems - A Lyapunov min-max approach. IEEE Trans. Automat. Control 24 (1979), 437-443. · Zbl 0416.93076 |

[4] | J. K. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York 1977. · Zbl 1092.34500 |

[5] | J. K. Hale and S. M. V. Lunel: Introduction to Functional Differential Equations. Springer-Verlag, New York 1993. |

[6] | T. H. Hopp and W. E. Schmitendorf: Design of a linear controller for robust tracking and model following. ASME J. Dyn. Syst. Measurement Control 112 (1990), 552-558. · Zbl 0747.93022 |

[7] | V. B. Kolmanovskii and V. R. Nosov: Stability of Functional Differential Equations. Academic Press, London 1986. |

[8] | S. Oucheriah: Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers. IEEE Trans. Automat. Control 44 (1999), 1473-1577. · Zbl 0955.93026 |

[9] | S. Shigemaru and H. Wu: Decentralized robust tracking and model following for uncertain large-scale interconnected systems. J. Optim. Theory Appl. 110 (2001), 35-52. · Zbl 0979.93005 |

[10] | K. K. Shyu and Y. C. Chen: Robust tracking and model following for uncertain time-delay systems. Internat. J. Control 62 (1995), 589-600. · Zbl 0830.93026 |

[11] | T. Sugie and K. Osuka: Robust model following control with prescribed accuracy for uncertain nonlinear systems. Internat. J. Control 58 (1993), 991-1009. · Zbl 0787.93034 |

[12] | H. Wu: Eigenstructure assignment based robust stability conditions for uncertain systems with multiple time-varying delays. Automatica 33 (1997), 97-102. · Zbl 0886.93049 |

[13] | H. Wu: Continuous adaptive robust controllers guaranteeing uniform ultimate boundedness for uncertain nonlinear systems. Internat. J. Control 72 (1999), 115-122. · Zbl 0945.93019 |

[14] | H. Wu: Adaptive stabilizing state deedback controllers of uncertain dynamical systems with multiple time delays. IEEE Trans. Automat. Control 45 (2000), 1697-1701. · Zbl 0990.93119 |

[15] | H. Wu: Robust tracking and model following control with zero-tracking error for uncertain dynamical systems. J. Optim. Theory Appl. 107 (2000), 169-182. · Zbl 0999.93062 |

[16] | H. Wu: Design of memoryless controllers for robust tracking and model following of uncertain systems with multiple time delays. IEEJ Trans. Electronics, Informat. Systems 121 (2001), 1268-1276. |

[17] | H. Wu: Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections. IEEE Trans. Automat. Control 47 (2002), 1745-1751. · Zbl 1364.93673 |

[18] | H. Wu: Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays. IEEE Trans. Automat. Control 49 (2004), 611-616. · Zbl 1365.93227 |

[19] | H. Wu and K. Mizukami: Robust stability criteria for dynamical systems including delayed perturbations. IEEE Trans. Automat. Control 40 (1995), 487-490. · Zbl 0821.93060 |

[20] | H. Wu and K. Mizukami: Linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay. IEEE Trans. Automat. Control 41 (1996), 116-121. · Zbl 0842.93065 |

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