Riesz-thorin and the l_p stability of nonlinear time varying feedback systems

Abstract

The paper is concerned with the L_pstability of a class of nonlinear time varying feedback systems, with a linear time invariant stable part g in feedback with a nonlinear time varying gain k(t)y(.). The Riesz - Thorin interpolation theorem is employed in a novel way to derive the L_p-stability conditions (for 1≤p≤∞) which are believed to be more general and less restrictive than the results of the literature. These conditions involve a (cau–sal + anti–causal) multiplier function and global conditions on the normalized rate of variation of k(t)