不确定中立型随机多时滞系统的鲁棒H_∞控制

Robust H_∞ Control of Uncertain Neutral Stochastic Systems with Multiple Time Delays

研究一类具有参数不确定性的中立型随机多时滞系统的鲁棒镇定和鲁棒H_∞控制问题。设计了具有分布时滞的状态反馈H_∞控制器,通过构造Lyapunov泛函,由Ito公式,并利用Schur补原理,建立了用线性矩阵不等式表示的保证闭环系统随机渐近稳定的时滞依赖的充分条件。进一步给出了不确定系统鲁棒H_∞控制可解性的时滞依赖的充分条件。通过求解线性矩阵不等式,得出了中立型随机时滞系统的具有分布时滞的状态反馈H_∞控制器。数值仿真证明了该方法的有效性。

The problem of robust stabilization and robust Hoo control for a class of neutral stochastic systemswith multiple time delays and norm-bounded parameter uncertainties is studied. The controller withdistributed delays is considered, based on the Lyapunov functional, Ito formula and Schur theory, the delaydependent sufficient conditions which ensures the closed-loop system asymptotically stable are established.Furthermore, the delay dependent sufficient conditions are obtained for the solvability of robust Hoo controlof the uncertain system. The state feedback Hoo controller with distributed delays of the stochastic delaysystem is designed by solving the linear matrix inequality. The numerical example is provided to illustratethe effectiveness of the proposed design method.