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.
Discontinuous Integral Control for Systems with Arbitrary Relative Degree
Studies in Systems, Decision and Control
2020-02-11
41 pages
Article/Chapter (Book)
Electronic Resource
English
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