Stability and Performance Analysis of Control Systems Subject to Bursts of Deadline Misses

Control systems are by design robust to various disturbances, ranging from noise to unmodelled dynamics. Recent work on the weakly hard model---applied to controllers---has shown that control tasks can also be inherently robust to deadline misses. However, existing exact analyses are limited to the stability of the closed-loop system. In this paper we show that stability is important but cannot be the only factor to determine whether the behaviour of a system is acceptable also under deadline misses. We focus on systems that experience bursts of deadline misses and on their recovery to normal operation. We apply the resulting comprehensive analysis (that includes both stability and performance) to a Furuta pendulum, comparing simulated data and data obtained with the real plant. We further evaluate our analysis using a benchmark set composed of 133 systems, which is considered representative of industrial control plants. Our results show the handling of the control signal is an extremely important factor in the performance degradation that the controller experiences---a clear indication that only a stability test does not give enough indication about the robustness to deadline misses.