Practical L2 disturbance attenuation for nonlinear systems

Abstract

In this work, a notion of generalized L 2-gain for nonlinear systems, where the gain is considered as a function of the state instead of a (global) constant, is presented. This new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform L 2-gain property (i.e. the L 2-gain depends on the operating point). Moreover, a notion of practical L 2-gain attenuation, which extends the standard definition and parallels (mutatae mutandis) the concepts of practical stability, is also proposed.