Global non-fragile and fixed-time output-feedback stabilisation for nonlinear systems with measurement noise

In this paper, the problem of global non-fragile and fixed-time output-feedback stabilisation is considered for a class of nonlinear systems with a lower-triangular form and uncertain measured noise. First, two Lyapunov matrix inequalities with uncertainties are presented. Then, a positive and a negative homogeneous system with unknown perturbations are given and proven to be globally asymptotically stable and finite-time stable, respectively, based on these two matrix inequalities. Besides, two homogeneous Lyapunov functions are constructed, and two important Lyapunov inequalities are derived. Second, by applying an auxiliary variable, the considered nonlinear system is augmented. Then, a non-fragile augmented output-feedback controller, incorporating positive and negative homogeneous terms, is presented to ensure the fixed-time stability of the closed-loop system. Finally, two simulation examples are used to verify the effectiveness of the proposed control scheme.