Output-feedback control of stochastic strict-feedback systems under an exponential cost criterion

We consider a class of single-input single-output stochastic nonlinear systems in strict-feedback form with a risk sensitive cost criterion and with only the output of the system being available for feedback. We design an output-feedback controller under which the closed-loop signals maintain an arbitrarily small average risk-sensitive cost. Moreover, all closed-loop signals remain bounded in probability, and under certain conditions we obtain asymptotic stability in probability.