Continuous output feedback stabilization for a class of stochastic high-order nonlinear systems

This paper is concerned with the problem of the global control design via output feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and unknown control coefficients. In fact, there have been many deterministic results which inspired the recent intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions of the systems, there lack basic concepts and theorems for the problem to be solved here. First of all, two stochastic stability concepts are extended to allow the systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense (see also [24]). Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, an continuous (nonsmooth) output feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability. It should be pointed out that the paper is motivated by the recent non-stochastic works of C. J Qian´s group.