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。

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.

This paper addresses the design problem of practical (or satisfaction) output-feedback controls for stochastic strict-feedback nonlinear systems in observer canonical form with stable zerodynamics under long-term average tracking risk-sensitive cost criteria. The cost function adopted here is of the quadratic-integral type usually encountered in practice, rather than the quartic-integral one used to avoid difficulty in control design and performance analysis of the closed-loop system. A sequence of coordinate diffeomorphisms is introduced to separate the zero-dynamics from the entire system, so that the transformed system has an appropriate form suitable for integrator backstepping design. For any given risk-sensitivity parameter and desired cost value, by using the integrator backstepping methodology, an output-feedback control is constructively designed such that (a) the closed-loop system is bounded in probability and (b) the long-term average risk-sensitive cost is upper bounded by the desired value. In addition, this paper does not require the uniform boundedness of the gain functions of the system noise. Furthermore, an example is given to show the effectiveness of the theory.

究了离散时滞系统的一种低阶l12控制问题。得到了系统可实现状态反馈及输出反馈l12控制的充分条件，并将其转化为线性矩阵不等式（LMI）形式，给出了l12控制的显式表达形式。文中的处理不是转化为无穷维受限优化问题，而是优化l12范数的一上界。尽管得到的是次优l12控制律，但由于它具有确定的结构，故分析和设计过程十分简单。

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.