Observability of linear stochastic uncertain systems

A concept of observability of uncertain systems has received some attention in the recent literature. In this note, we extend this concept to stochastic uncertain systems. We show that the observability of a stochastic uncertain system can be characterized using a relative entropy functional which plays the same role as the observability Gramian plays in linear system analysis. Also, we establish a connection between the observability of a linear stochastic uncertain system under consideration and risk-sensitive performance of an associated reference system.