Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to alterations of the control signal pattern, due to sporadic late completions (called deadline misses) when implemented as a digital task on an embedded platform. Recent research analysed stability when imposing constraints on the maximum number of consecutive deadlines that can be missed. This is only one type of characterization, and results in a pessimistic analysis when applied to more general cases. To overcome this limitation, this paper proposes a comprehensive stability analysis for control systems subject to a set of generic constraints, describing the possible sequences of correct completions and deadline misses. The proposed analysis brings the assessment of control systems robustness to computational problems one step closer to the controller implementation.