Nonlinear systems with nonlinear L2-gain

Abstract

Nonlinear 2-gain is a robust stability property whereby the 2-norm of the state trajectory is bounded above by a monotone aggregation of nonlinear scalings of the norm of the initial state and the 2-norm of the input. This property is equivalent, via a change of coordinates, to integral input-to-state stability. In order to better understand the nonlinear 2-gain property, a variety of simple examples are presented for which it is possible to explicitly calculate the attendant transient and gain bounds. A constructive approach to finding changes of coordinates that yield systems satisfying the linear or nonlinear 2-gain property is also illustrated by example.