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.

Automated summary

This study demonstrates that coupling any homogeneous controller with the proposed robust homogeneous filtering observer can achieve asymptotic stabilization of disturbed integrator chains. The type of convergence is determined by the sign of the system homogeneity degree, with different cases corresponding to zero and negative HDs. The study also shows accurate stabilization and differentiation in the presence of unbounded sampling noises with locally bounded iterated integrals.