This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example.
Keywords: Markovian switching; output-feedback; stabilization; stochastic nonlinear systems; time-varying powers.