Rejection of persistent /spl Lscr//sub /spl infin//-bounded disturbances for nonlinear systems

A nonlinear /spl Lscr//sup 1/-control problem, which deals with the rejection of persistent bounded disturbances for nonlinear systems, is investigated. The concept of invariance plays an important role in the /spl Lscr//sup 1/-performance analysis and synthesis. The main idea is to construct an invariant subset in the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to the subset. 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 system is established.