The risk-sensitive index and the \(H_ 2\) and \(H_ \infty\) norms for nonlinear systems (Q1913679)

This paper deals with \(H_\infty\) and \(H_2\) norms which are important tools for determining the influence of disturbances on the performance. The authors introduce the \(H_\infty\) and \(H_2\) norms and the risk-sensitive index for nonlinear system, as a natural generalization of the linear case, and they investigate the relationship between them. In particular, they show that the \(H_\infty\) (resp. \(H_2)\) norm is the small noise (resp. risk) limit of the risk-sensitive index and they compute them using directional derivatives of the risk-sensitivity index.