中立型随机时滞系统的时滞依赖鲁棒非脆弱H_∞控制

Delay-Dependent Non-Fragile Robust H_∞ Control of Neutral Stochastic Time-Delay Systems

针对一类中立型随机时滞系统,本文利用随机Lyapunov稳定理论和Ito微分法则,研究了其非脆弱镇定和H∞控制问题。在控制器增益分别具有加法式摄动和乘法式摄动的情形下,推导出系统随机鲁棒可镇定和鲁棒H∞控制器存在的充分条件。通过求解线性矩阵不等式(linear matrix ine qualities,LMI),设计了中立型随机时滞系统的记忆状态反馈非脆弱控制器,并给出控制器的存在条件是时滞依赖。数值仿真结果表明,此控制器使中立型随机时滞系统的鲁棒性是随机稳定的,且具有干扰衰减系数γ∞。

The problems of non-fragile stabilization and H∞ control for a class of neutral stochastic systems with state delay is investigated by means of stochastic Lyapunov stability theory and Ito differential rule. Under two kinds of controller gain disturbance, the sufficient conditions are derived for the robust stabilization and the existence of robust H∞ controller. The memory state feedback non-fragile H∞ controller of neutral stochastic delay system is designed by solving linear matrix inequalities（LMI）. Also, the condition given in this paper is delay-dependent. Finally, a numerical example is given to illustrate that the closedloop stochastic system is robustly stochastically stabilizable with disturbance attenuation level γ∞.