Global output feedback stabilization for a class of uncertain stochastic nonlinear retarded systems with Markovian switching

The global output feedback stabilization for a class of uncertain stochastic nonlinear retarded systems with Markovian switching is studied in this paper. The conditions under which the analytical solution is existed uniquely and the equilibrium is globally asymptotically stable are obtained. Then, for the systems with uncertain parameters which exists in both drift and diffusion coefficients, an output feedback controller is constructively designed to make the closed-loop system globally asymptotically stable by the backstepping method. The results obtained in the paper extend the existing methodology of stochastic retarded system to stochastic retarded system with Markovian switching. And the virtual controls and control are nonlinear functions about Markov chain. At last, an example is given to illustrates the effectiveness of the proposed output feedback control approach.