For systems with arbitrary relative degree, we propose a homogeneous controller capable of tracking a smooth but unknown reference signal, despite a Lipschitz continuous perturbation, and by means of a continuous control signal. The proposed control scheme consists of two terms: (i) a continuous and homogeneous state feedback and (ii) a discontinuous integral term. The state feedback term aims at stabilizing (in finite time) the closed-loop while the (discontinuous) integral term estimates the perturbation and the unknown reference signal in finite time and provides for perfect compensation in closed loop. By adding an exact and robust differentiator, we complete an output feedback scheme, when only the output is available for measurement. The global finite-time stability of the closed-loop system and its insensitivity with respect to the Lipschitz continuous perturbations are proved in detail using several (smooth) homogeneous Lyapunov functions for different versions of the algorithm.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Discontinuous Integral Control for Systems with Arbitrary Relative Degree


    Additional title:

    Studies in Systems, Decision and Control




    Publication date :

    2020-02-11


    Size :

    41 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English






    New Simple Adaptive Control Algorithms in Case of Arbitrary Relative Degree

    Mine, M. / Date, K. / Ohmori, H. et al. | British Library Conference Proceedings | 2000


    Tracking Control of Nonlinear Systems with No Relative Degree

    Yamashita, Y. / Onishi, N. / Nishitani, H. | British Library Online Contents | 2002


    Degree Distribution of Arbitrary AANET

    Xue Liu / Xiaoping Zeng / Zhiming Wang et al. | DOAJ | 2015

    Free access