Filtering homogeneous observers in control of integrator chains

Any homogeneous controller asymptotically stabilizing disturbed integrator chains can be coupled with the proposed robust homogeneous filtering observer. The type of convergence (in finite-time, in fixed-time to any ball or exponential) is determined by the sign of the system homogeneity degree (HD). Filtering high-gain observers and sliding-mode-based observers/differentiators are important particular cases corresponding to zero and negative HDs, respectively. Stabilization accuracy is estimated in the presence of possibly unbounded sampling noises featuring locally bounded iterated integrals. Accurate stabilization and differentiation are demonstrated for extremely large noises.