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研究了一类具有参数不确定性的中立型随机时滞系统的鲁棒非脆弱镇定和鲁棒非脆弱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,通过构造Lyapunov泛函,利用Ito公式和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均方渐近稳定的充分条件;给出了不确定系统鲁棒非脆弱H∞控制可解性的充分条件;通过求解线性矩阵不等式,设计了随机时滞系统的记忆状态反馈非脆弱H∞控制器。数值仿真证明了该方法的有效性。
We study the robust non-fragile stabilization and robust non-fragile H∞ control problem for a class of neutral stochastic systems with parametric uncertainties. In the case that the controller gain has additive perturbation and multiplicative perturbation respectively, by constructing Lyapunov functional and using Ito formula and Schur complement principle, the system of asymptotically stable random systems with closed-loop systems guaranteed by linear matrix inequalities The sufficient conditions for the robust and non-fragile H∞ control of an uncertain system are given. The memory state feedback non-fragile H∞ controller for stochastic systems with time-delay is designed by solving the linear matrix inequalities. Numerical simulation proves the effectiveness of this method.