Stabilization of networked control systems with weakly hard real-time dropout description

The usage of weakly hard real-time constraints to model the loss process in Networked Control Systems aims for studying more realistic network models, while still being able to guarantee stability in the sense of Lyapunov. An open question is, whether it is possible to find a stabilizing controller for a given loss specification, which is the main question of the study at hand. It is formalized as the problem of state feedback stabilizability under weakly hard real-time constraints. To solve the problem, stability conditions for switched systems employing switched Lyapunov functions that have already been shown to be suitable for studying arbitrary bounded packet losses are extended towards the consideration of constrained switching sequences. Those sequences for the weakly hard real-time constraints are represented by a labeled graph that highly relies on an auxiliary system with a restricted, suitably chosen discretization. The overall result shows to be effective in a numerical example.