一类离散时滞系统的极小极大鲁棒控制

针对一类离散时滞系统设计有记忆的状态反馈控制器,使得在最坏的干扰和不确定性下,闭环系统渐近稳定且性能指标存在一个最小上界.给出离散时滞系统的极小极大控制定义,利用李亚普诺夫方法和线性矩阵不等式(LMI)方法给出了极小极大鲁棒控制器的存在条件和设计方法.通过建立、求解凸优化问题得到最优极小极大控制器参数和性能指标的最小上界.最后给出数值算例,说明所设计的极小极大控制器只需付出较小的代价成本就能很好地抑制干扰.

Minimax Robust Control of a Class of Discrete Systems with Time-Delay

For a class of discrete systems with time-delay,a memorial state feedback controller is designed to enable the closed-loop system to be asymptotically stable with a minimum upper bound assigned to the performance index involving the worst uncertainty or disturbance.Defining the minimax robust control of discrete time-delay systems,the existence condition and design method of minimax robust controller are given by the Lyapunov method and LMI(linear matrix inequation).Then by building and solving the convex optimization problem,the optimal upper bound of performance index and parameters of the state feedback controller is given.Some numerical examples are shown to illustrate that the minimax controller can prevent well from disturbance at little expense.