Integral-augmented finite-time control of nonlinear systems with frequency-domain analysis

Integral action is routinely incorporated in modern control frameworks through state augmentation to eliminate steady-state errors. However, for nonlinear systems requiring faster converging speed and strong disturbance rejection, the systematic design of integral action with nonlinear control and frequency-domain tuning remains insufficiently investigated. This paper proposes a nonlinear finite-time integral-action control strategy for a class of affine nonlinear systems subject to matched disturbances. By employing feedback linearisation, the closed-loop dynamics are transformed into an equivalent integral chain structure, under which finite-time stability is rigorously established via Lyapunov analysis. A characterisation of the disturbance-dependent bounded stable region is also provided. To facilitate controller gain tuning and robustness assessment, the proposed nonlinear closed-loop system is further analysed from a frequency-domain perspective using a linear parameter-varying (LPV) framework. This approach enables the evaluation of classical robustness metrics and the closed-loop pole behaviour in the complex plane. Finally, simulations on a DC-DC converter demonstrate the effectiveness of the proposed method.