带随机扰动的时滞系统的鲁棒H_∞控制

Robust H_∞ Control of Discrete Time-delay Systems with Stochastic Perturbation

研究了一类带随机扰动的时滞系统的状态反馈鲁棒控制的问题,其中系统的系数矩阵为随机矩阵,且假设不确定参数矩阵是时变、范数有界的。借助于线性矩阵不等式(LMI),给出了系统是鲁棒可镇定的充分条件,并设计了一个状态反馈控制器,使得闭环系统均方渐近稳定,且满足给定的性能指标。

This paper deals with the problem of robust control for discrete time-delay systems with stochastic perturbation and norm-bounded parameter uncertainties.The model mentioned above is a particular case of the general time-delay systems for its stochastic state matrices.First of all,we investigate mean-square asymptotic stability of the systems.The sufficient conditions of the problem are obtained by solving certain LMIs.Secondly,based on the stability result,the controllers are designed respectively to stabilize the system for all admissible uncertainties and satisfied corresponding performance.Finally,an example is provided to demonstrate the effectiveness of the proposed approach.