A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, unmodelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the estimation errors are analyzed. In addition, by using the integrator backstepping approach, an output-feedback stabilization control is constructively designed, and suf cient conditions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.

In this paper, the design problem of satisfaction output feedback controls for stochastic nonlinear systems in strict feedback form under long-term tracking risk-sensitive index is investigated. The index function adopted here is of quadratic form usually encountered in practice, rather than of quartic one used to beg the essential difficulty on controller design and performance analysis of the closed-loop systems. For any given risk-sensitive parameter and desired index value, by using the integrator backstepping method, an output feedback control is constructively designed so that the closed-loop system is bounded in probability and the risk-sensitive index is upper bounded by the desired value.

In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.

对一类具有不可观测状态、未建模动态特性和随机干扰的单输入多输出随机非线性系统，给出了最小阶状态观测器和输出反馈镇定控制器的设计方法。基于所设计的最小阶状态观测器，给出了系统全部状态的估计，分析了状态估计误差的收敛性。进一步，结合Back-Stepping法，构造性地设计出了输出反馈镇定控制，给出了闭环系统全局渐近稳定和概率意义下有界稳定的充分条件。

在无限时区跟踪型风险灵敏度（risk-sensmve）指标下，研究了一类严格反馈随机非线性系统的满意输出反馈控制问题。所用指标函数为实际中常见的二次型函数，而非为回避控制器设计及闭环系统性能分析的本质困难而采用的四次型函数。对任意给定的风险灵敏度参数和期望指标值，利用积分反推（integratorbackstepping）方法构造性地给出了一个输出反馈控制器，使得闭环系统在概率意义下有界，并且风险灵敏度指标不大于所给的期望值。