Control and observer design for stochastic bilinear systems with delays

This paper considers controller design and observer design for Itô-type stochastic bilinear delay systems. First, we consider the stability of closed-loop bilinear stochastic delayed systems by introducing a nonlinear controller. A sufficient mean square asymptotically stability condition is established, which is given in terms of linear matrix inequality (LMI). Then, the problem of observer design for the systems under consideration is investigated. By defining a Luenberger observer, a sufficient condition is given, which enables the resulting error system to be asymptotically stable in the mean-square sense, and an observer design method is proposed. Finally a numerical example is provided to show the validity of the approach.