Integral Control Design using the Implicit Lyapunov Function Approach

In this paper, we design homogeneous integral controllers of arbitrary non positive homogeneity degree for a system in the normal form with matched uncertainty/perturbation. The controllers are able to reach finite-time convergence, rejecting matched constant (Lipschitz, in the discontinuous case) perturbations. For the design, we use the Implicit Lyapunov Function method combined with an explicit Lyapunov function for the addition of the integral term.

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