A novel fixed-time <i>H</i> _<i>∞</i> control for <i>p</i> -normal form nonlinear systems with disturbances

This paper considers the fixed-time H ∞ stabilization for p -normal form nonlinear systems with external disturbances. A special local smooth nonlinear function (LSNF) is introduced, and a new lemma about the LSNF is given first. Based on the lemma, the fixed-time control and the H ∞ control, a novel improved H ∞ control strategy is proposed, and the robust fixed-time H ∞ controller is obtained, which presets the upper bound of the cost function (UBCF) of the output. It should be emphasized that the preseted UBCF is completely independent of the disturbances and even the system initial values rather than dependent on the disturbances like most general H ∞ control strategies, which greatly enhances the robustness of the H ∞ control. Moreover, the controller results in a globally fixed-time stable closed-loop system when the external disturbances are nonexistent. Finally, to prove the effectiveness and the practicability of the improved H ∞ control strategy, two simulation examples, including a planetary gear-type inverted-pendulum (PGTIP), are given.