Robust Stability and Performance of Stochastic Uncertain Systems on an Infinite Time Interval

In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative. 1 Introduction Consider an uncertain system involving an LFT type interconnection between the nominal system model and the uncertainty in the system [5]; see Figure 1. Given a set of admissible uncertainties #(s), the problem of robust stability with guaranteed performance is to evaluate the stability and worst-case performance of th..