Abstract
AbstractIn this article, continuous and discontinuous integral controllers for multiple‐input multiple‐output (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 nonvanishing Lipschitz matching perturbations. Continuous integral controllers achieve asymptotic stabilization despite nonvanishing 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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