Linear Weakly Hard Real-Time Control Systems: Time- and Event-Triggered Stabilization

This article considers the stabilization of linear control systems under weakly hard real-time (WHRT) constraints. In the context of networked control systems, such WHRT constraints allow us to specify packet loss properties of a communication network over windows of a given length, e.g., at least
n
consecutive transmissions in every window of
m
consecutive transmission attempts are successful. Time- and event-triggered stabilization results are derived. The control design exploits a graph that captures the available information on possible packet losses. An algorithm for computing such a graph for given WHRT constraints is provided. Both stabilization results are illustrated and compared using a numerical example from literature.