"Attenuation of Persistant L--Bounded Disturbances for Nonlinear SystemsT9

A version of nonlinear generalization of the C1-control problem, which deals with the attenuation of persistent bounded disturbances in &-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the C1-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. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the C1-control of a continuous-time system and the el-control of its Euler approximated discrete-time systems is established. K e y Words: Controlled Invariance, Disturbance Rejection, C1 Optimal Control, Nonlinear Systems, Robust Control.