This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee$\mathcal {L}_{2}$-stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. Note to Practitioners—With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co- design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

In this paper, a dynamic zero-sum game is formulated to describe the power decision-making process of the sensor/relay and the DoS attacker in cyber-physical systems. The sensor and the relay cooperate with each other to transmit the state estimation to the remote estimator, when the attacker, on the contrary, aims to disturb the wireless communication channels strategically for deterioration of the system performance but can do this taking into account its limited energy. Different from conventional battery-powered nodes, the sensor and the relay can harvest energy from the external environment and store it in their batteries for data transmission. We model the external environment state as a Markov chain to overcome the randomness of the harvested energy. In addition, to tackle the computation complexity of the Nash equilibrium (NE), we restrict our attention to a special case, i.e., the DoS attacker can only launch interference on one of the two communication channels over an infinite time horizon, and provide the corresponding NE strategy of the game using the Markov decision process and the multi-agent reinforcement learning algorithm. Finally, simulation examples are given to illustrate the theoretical findings of the paper.