Asynchronous hybrid event- and time-triggered control of heterogeneous networks with communication time delays.

This paper addresses the asynchronous leader-following consensus problem for networked double-integrator systems. In practical engineering contexts, there are three key factors that must be considered significantly: (1) asynchronous hybrid event- and time-triggered control, where asynchrony affects event detection, event-triggered processes, and controller updates; (2) heterogeneous networks, wherein position and velocity information are governed by distinct, independent graphs; and (3) communication time delays arising from limited bandwidth and long-distance transmission. Due to the independence of these heterogeneous networks, edge events related to position and velocity information are defined separately. When an event occurs on an edge, the connected agents sample the corresponding relative state information (position or velocity) and update their controllers accordingly. The paper proposes a control protocol based on these event rules and employs Lyapunov methods to address the leader-following consensus problem. Numerical simulations are provided to validate and illustrate the theoretical findings.