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MIMO Homogeneous Integral Control Design using the Implicit Lyapunov Function Approach

Abstract : In this paper, continuous and discontinuous integral controllers for MIMO systems are designed for a large class of nonlinear systems, which are (partially) feedback linearizable. These controllers of arbitrary positive or negative degree of homogeneity are derived by combining a Lyapunov function obtained from the Implicit Lyapunov Function (ILF) method with some extra explicit terms. Discontinuous integral controllers are able to stabilize an equilibrium or track a time-varying signal in finite time, while rejecting vanishing uncertainties and non-vanishing Lipschitz matching perturbations. Continuous integral controllers achieve asymptotic stabilization despite non-vanishing constant perturbations in finite-time, exponentially or nearly fixed-time for negative, zero or positive homogeneity degree, respectively. The design method and the properties of the different classes of integral controllers are illustrated by means of a simulation example.
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Contributor : Andrey Polyakov Connect in order to contact the contributor
Submitted on : Thursday, February 4, 2021 - 3:01:22 PM
Last modification on : Friday, January 21, 2022 - 3:12:18 AM
Long-term archiving on: : Wednesday, May 5, 2021 - 7:04:33 PM


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Angel Mercado-Uribe, Jaime Moreno Pérez, Andrey Polyakov, Denis Efimov. MIMO Homogeneous Integral Control Design using the Implicit Lyapunov Function Approach. International Journal of Robust and Nonlinear Control, Wiley, 2021, ⟨10.1002/rnc.5474⟩. ⟨hal-03131618⟩



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