Decentralized Resilient H ∞ Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks Xin Zhao, Suli Zou, Member, IEEE, and Zhongjing Ma, Senior Member, IEEE Abstract—This paper designs a decentralized resilient H ∞ load frequency control (LFC) scheme for multi-area cyber-physical power systems (CPPSs). Under the network-based control framework, the sampled measurements are transmitted through the communication networks, which may be attacked by energy- limited denial-of-service (DoS) attacks with a characterization of the maximum count of continuous data losses (resilience index). Each area is controlled in a decentralized mode, and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area. Then, the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances. Under this modeling, a decentralized resilient H ∞ scheme is presented to design the state-feedback controllers with guaranteed H ∞ performance and resilience index based on a novel transmission interval-dependent loop functional method. When given the controllers, the proposed scheme can obtain a less conservative H ∞ performance and resilience index that the LFC system can tolerate. The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks. Index Terms—Cyber-physical power systems (CPPSs), denial-of- service (DoS) attacks, load frequency control (LFC), sampled-data control.    I. Introduction W ITH the developments of smart grids, advanced sensors, communication and control techniques have been widely applied in the operation of power systems, where traditional power systems are gradually integrated with information control equipment and communication and sensor networks to evolve as cyber-physical power systems (CPPSs) [1]. To operate multi-area CPPSs smoothly, the LFC operation is widely used to restore the balance between generation and load in each control area for maintaining system frequency and power interchanges with other areas at scheduled values [2]. Thus, the LFC design of CPPSs has drawn lots of attention in recent years because there exists some hot issues [2 s, 4 s] [0.08 s, 0.3 s] in the cyber layer such as network-induced delay [3]–[5], communication bandwidth constraints, cyber attacks [6]–[9], and so on. In the framework of networked control system, sampled-data based LFC is often implemented such that the system contains a continuous-time process and discrete-time controller. For sampled-data LFC scheme, one way is to design it in continuous-time mode, and then implement it in a sampled-data manner, such as in, H ∞ control method [10], the pole assignment method [11], and unified PID turning scheme for LFC based on internal model control method [12]. But, the aforementioned LFC schemes are effective for a small enough sampling period. Another method is to design sampled-data LFC scheme based on the discrete LFC system, for example, event-triggered sliding mode LFC scheme [13], decentralized sliding mode LFC design considering time delay and wind power [14], and digital PID-type LFC design [15]. These results are obtained by regarding the sampling period as a discrete step. However, in practical LFC operations, the discrete LFC system may be infeasible to restore the real dynamic of the original system because the sampling period is generally set in the interval [2] under which the discrete period cannot satisfy Shannon sampling principle when time constants lying in internal in hydrothermal power system [2]. [2 s, 4 s] In order to avoid the two shortages above, an input-delay method is proposed to investigate the control design of sampled-data systems for avoiding discrete distortion [16]. As an improvement, a looped-functional method is proposed in [17] and further extended in [18]. Based on this method, the stability of LFC systems with both sampling and transmission delay is analyzed for different given PI controllers [19], and a robust LFC design considering both sampling period and transmission delay is proposed in [20]. Considering the penetration of wind power, a sampled-data and fast LFC scheme is proposed for multi-area power systems in [21], which focuses on the inner stability of LFC systems without taking the effects of load disturbances into account. Especially, for a typical sampling period of in the practical LFC operations, it is necessary to develop sampled- data LFC schemes which considers sampling information and load disturbances. In the cyber layer, when open communication infrastru- ctures are employed to complete the information exchange between power plants and LFC center, it has the benefits of low cost and high flexibility [22]. However, open communi- Manuscript received October 12, 2020; revised December 21, 2020; accepted February 27, 2021. This work was supported by the National Natural Science Foundation (NNSF) of China (62003037, 61873303). Recommended by Associate Editor Zhen Song. (Corresponding author: Zhongjing Ma.) Citation: X. Zhao, S. L. Zou, and Z. J. Ma, “Decentralized resilient H ∞ load frequency control for cyber-physical power systems under DoS attacks,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 11, pp. 1737–1751, Nov. 2021. The authors are with the School of Automation, Beijing Institute of Technology, Beijing 100081, China (e-mail: xinzhaofir@163.com; sulizou@bit.edu.cn; mazhongjing@bit.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2021.1004162 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 11, NOVEMBER 2021 1737