时滞相关不确定随机系统的鲁棒H_∞控制

Delay-dependent robust H_∞ control for uncertain stochastic systems

针对具有时变时滞和范数有界不确定性的随机系统,研究其随机镇定和鲁棒H∞控制问题.设计状态反馈控制器,使得对所有可容许的不确定性,闭环系统随机稳定且满足给定的H∞性能指标.利用线性矩阵不等式(LMI)及自由权矩阵技术得到系统镇定的一个充分条件,该充分条件由一组时滞相关的矩阵不等式表达.最后通过仿真数例表明了所提出方法的有效性.

This paper deals with the problems of robust stochastic stabilization and robust H∞ control for uncertain stochastic systems with a time-varying delay in the state and norm-bounded uncertainty. The problem is to design state feedback controllers such that the resulting closed-loop system is mean-square asymptotically stable for all admissible uncertainties, as well as satisfying a prescribed H∞ performance. Delayed-dependent sufficient conditions for the stability of the system are derived by using linear matrix inequalities and introducing free weighting matrices. Finally, numerical examples show the effectiveness of the proposed method.