This paper addresses a novel robust gain-scheduling(GS) state-feedback (SF) ${\mathcal{H}}_{\infty }$ (induced ${\mathcal{L}}_2$) control method for uncertain continuous-time(CT) systems having actuators with hard rate and magnitude bounds. The proposed method relies on acceleration form representation of the uncertain CT system. The technique enables the user to represent the control signal and its slew rate as auxiliary outputs along with the main controlled output. Two different norms, namely the induced ${\mathcal{L}}_{\infty }$ and ${\mathcal{L}}_2$ are used to control the system effectively. While the ${\mathcal{L}}_{\infty }$ gain from the exogenous disturbance inputs to the control signal related outputs is used to deal with actuator saturation problem, ${\mathcal{L}}_2$ gain from the disturbance inputs to the performance outputs is utilised in attenuation of the effects of the disturbances. To achieve these goals with minimal conservatism, we develop new forms of dilated Matrix Inequality (MI) conditions for peak-to-peak gain and ${\mathcal{L}}_2$ gain with no additional conservatism. Then, we propose a novel robust GS control methodology to deal with the problem via dilated MIs and a modified full block S-procedure method (MFBSPM). The utilisation of MFBSPM ensures that the robust control design method of this note applies to any uncertain system having rational parameter dependence. Finally, the efficiency of the presented method is portrayed through extensive simulations of the responses of a marine vessel to wave excitations in which the vessel model is assumed to have magnitude and rate limited active fin stabiliser.

本文讨论了一种新颖的鲁棒增益调度（GS）状态反馈（SF） ${\mathcal{H}}_{\infty }$ （诱导 ${\mathcal{升}}_2$) 具有硬速率和幅度界限的执行器的不确定连续时间 (CT) 系统的控制方法。所提出的方法依赖于不确定 CT 系统的加速度形式表示。该技术使用户能够将控制信号及其压摆率表示为辅助输出以及主控制输出。两种不同的规范，即诱导${\mathcal{升}}_{\infty }$ 和 ${\mathcal{升}}_2$用于有效控制系统。虽然${\mathcal{升}}_{\infty }$ 从外源干扰输入到控制信号相关输出的增益用于处理执行器饱和问题， ${\mathcal{升}}_2$从干扰输入到性能输出的增益用于衰减干扰的影响。为了以最小的保守性实现这些目标，我们开发了新形式的扩张矩阵不等式 (MI) 条件，用于峰峰值增益和${\mathcal{升}}_2$在没有额外的保守主义的情况下获得收益。然后，我们提出了一种新颖的鲁棒 GS 控制方法，通过扩张 MI 和改进的全块 S 过程方法（MFBSPM）来处理该问题。MFBSPM 的使用确保了本说明的鲁棒控制设计方法适用于任何具有合理参数相关性的不确定系统。最后，通过对船舶对波浪激励的响应的广泛模拟，描述了所提出方法的效率，其中假设船舶模型具有幅度和速率受限的有源鳍稳定器。