We study derivative-dependent control of the $n$th-order stochastic systems where derivatives are not available for measurements. The derivatives are approximated by finite differences giving rise to a delayed feedback. In the deterministic case, an efficient simple LMI-based method for designing of such static output-feedback and its sampled-data implementation was suggested recently. In the present paper, we extend this design to stochastic systems. We present two methods: the direct one that employs a stochastic extension of Lyapunov functionals used previously in the deterministic case, and the method which is based on neutral type model transformation and employs either augmented or simple Lyapunov functionals. Numerical examples illustrate the efficiency of the method.

我们研究了导数的控制 $ñ$导数不可用于测量的三阶随机系统。导数通过有限差分近似，从而引起延迟反馈。在确定性情况下，最近提出了一种有效的基于LMI的简单有效方法来设计此类静态输出反馈及其采样数据实现。在本文中，我们将这种设计扩展到了随机系统。我们提出两种方法：直接方法，该方法采用先前在确定性情况下使用的Lyapunov功能的随机扩展，以及基于中性类型模型转换并采用增强或简单Lyapunov功能的方法。数值算例说明了该方法的有效性。