Combined input–output finite-time stability condition with static output-feedback H_∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H_∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H_∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

本文提出了将输入输出有限时间稳定条件与静态输出反馈H _∞控制相结合，以有效地衰减短时道路扰动。控制问题是基于预先定义的输入输出有限时间稳定性条件H _{∞来表述的}与预先建立的四分之一车主动悬架模型结合在一起。然后，通过变量替换法和线性矩阵不等式设计了可行的静态输出反馈控制器。状态反馈技术解决了输出反馈控制最初不可行的问题。该控制器是专门为暴露于短时外源扰动的系统而设计的，因此，这项工作更喜欢有限时间方法而不是李亚普诺夫渐近稳定条件。为了列举所提出的控制器的重要性，给出了数值示例，并在不同的域（时间和频率）中有效地分析了其响应。理论结果表明，具有静态输出反馈H _{∞的组合输入输出有限时间稳定性条件}与被动和传统的静态输出反馈控制方案相比，控制可以更好地提高车辆性能。此外，还验证了控制器的鲁棒性。