The risk-sensitive index and theH2 andH∞, norms for nonlinear systems

In this paper we study two measures of the “size” of systems, namely, the so-calledH2 and H∞ norms. These measures are important tools for determining the influence of disturbances on performance. We show that the risk-sensitive index on an infinite time horizon contains detailed information concerning these measures, via small noise and small risk limits.

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