Robust properties of risk-sensitive control

The purpose of this paper is to characterize and prove robustness propertie s of risk-sensitive controllers precisely. In particular, we establish a st ochastic version of the small gain theorem. This theorem is expressed in te rms of an inequality which bounds the average output power in terms of the input power. Since this inequality is closely related to the risk-sensitive criterion, our stochastic small gain theorem can be expressed in terms of the risk-sensitive criterion. This provides a concrete motivation for the u se of the risk-sensitive criterion stochastic robustness.