A new perspective on robust performance for LQG control problems

This paper considers a class of discrete time, linear, stochastic uncertain systems defined in terms of a nominal Gaussian state-space model; the uncertainty is described by a relative entropy tolerance for each time increment of the dynamic model. For this class of systems, a problem of worst-case robust performance analysis with respect to a quadratic cost functional is solved. The solution takes the form of a risk-sensitive cost with a time-varying risk-sensitive parameter. Finally, a numerical example is presented to illustrate the methodology.