In this paper, the important issue is proposed, that is, the robust control of a class of cyber-physical systems (CPSs) in the complex environment where unknown disturbances, unknown bounded delays and stochastic malicious attacks coexist. A Lyapunov–Krasovskii functional (LKF) containing certain double and triple integral terms is constructed to exploit merits of the presented generalised single and double integral inequalities which are tighter than some existing single and double inequalities, leading to the stability analysis result with less conservatism. Furthermore, by using stochastic analysis technique, the stability analysis and $H_{\mathrm{\infty }}$ output feedback controller design are transformed into the convex optimisation problems solved by the linear matrix inequality (LMI) strategy. Finally, the actual load frequency control (LFC) power system and the classical numerical examples are provided to show the rationality for modelling and the advancement of the developed method.

本文提出了一个重要的问题，即在未知干扰，未知时延和随机恶意攻击共存的复杂环境中，对一类网络物理系统（CPS）的鲁棒控制。构造包含某些双整数和三阶积分项的Lyapunov–Krasovskii泛函（LKF），以利用所提出的广义单整数和双整数不等式的优点，该不等式比某些现有的单整数和双不等式更严格，从而导致稳定性分析结果的保守性较低。此外，通过使用随机分析技术，稳定性分析和$H_{\mathrm{\infty }}$输出反馈控制器设计被转化为通过线性矩阵不等式（LMI）策略解决的凸优化问题。最后，提供了实际负载频率控制（LFC）电力系统和经典的数值示例，以说明建模的合理性和所开发方法的改进。