Attenuation of persistent ℒ/sub ∞/-bounded disturbances for nonlinear systems

Abstract

A version of nonlinear generalization of the /spl Lscr//sup 1/-control problem, which deals with the attenuation of persistent bounded disturbances in /spl Lscr//sub /spl infin//-sense, is investigated in this paper. The main idea in the /spl Lscr//sup 1/-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. In addition, the relation between the /spl Lscr//sup 1/-control of a continuous time system and the l/sup 1/-control of its Euler approximated discrete-time systems is established.