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**Design of adaptive sliding mode controller for robust tracking and model following.**
*(English)*
Zbl 1214.93029

Summary: The problem of the robust tracking and model following for a class of linear systems with time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance is investigated in this paper. The algorithm is based on the adaptive sliding mode control. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. This scheme guarantees the closed-loop system stability and zero-tracking error in the presence of time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance. Finally, simulation results demonstrate the efficacy of the proposed control methodology.

### MSC:

93B12 | Variable structure systems |

93C40 | Adaptive control/observation systems |

93C05 | Linear systems in control theory |

93C73 | Perturbations in control/observation systems |

93D20 | Asymptotic stability in control theory |

### Keywords:

robust tracking; linear systems with time-varying parameter uncertainties; multiple delayed state perturbations; external disturbance; adaptive sliding mode control; closed-loop system stability
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\textit{M. C. Pai}, J. Franklin Inst. 347, No. 10, 1837--1849 (2010; Zbl 1214.93029)

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### References:

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