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研究了控制器增益在加法式摄动下的非脆弱鲁棒H∞控制问题,基于线性矩阵不等式(LMI)理论,提出了非脆弱鲁棒H∞控制器存在的充分条件,将具有控制器增益不确定性的非脆弱鲁棒控制器设计问题,化为具有线性矩阵不等式约束和线性目标函数的凸优化问题求解,得到了一种非脆弱鲁棒H∞状态反馈控制器的简化设计方法。所设计的控制器在容许的增益摄动下,仍能保证闭环系统的稳定性和性能要求,系统不仅具有鲁棒性而且是非脆弱的,从而使系统具有更高的可靠性。仿真结果表明了设计方法的有效性。
In this paper, we study the non-fragile robust H∞control problem of controller gain under additive perturbation. Based on the linear matrix inequality (LMI) theory, a sufficient condition for the existence of non-fragile robust H∞controller is proposed. The controller gain Uncertain non-fragile robust controller design problem is solved as a convex optimization problem with linear matrix inequality constraints and linear objective function. A simplified design method of non-fragile robust H∞ state feedback controller is obtained. The designed controller can still guarantee the stability and performance requirements of the closed-loop system under the allowable gain perturbation. The system is not only robust but also non-fragile, which makes the system more reliable. Simulation results show the effectiveness of the design method.