Error-energy bounds for adaptive gradient algorithms

The paper establishes robustness, optimality, and convergence properties of the widely used class of instantaneous-gradient adaptive algorithms. The analysis is carried out in a purely deterministic framework and assumes no a priori statistical information. It employs the Cauchy-Schwarz inequality for vectors in an Euclidean space and derives local and global error-energy bounds that are shown to highlight, as well as explain, relevant aspects of the robust performance of adaptive gradient filters (along the lines of H^∞ theory)