Control-System Stability Under Consecutive Deadline Misses Constraints

17 This paper deals with the real-time implementation of feedback controllers. In particular, it provides 18 an analysis of the stability property of closed-loop systems that include a controller that can 19 sporadically miss deadlines. In this context, the weakly hard m-K computational model has been 20 widely adopted and researchers used it to design and verify controllers that are robust to deadline 21 misses. Rather than using the m-K model, we focus on another weakly-hard model, the number of 22 consecutive deadline misses, showing a neat mathematical connection between real-time systems 23 and control theory. We formalise this connection using the joint spectral radius and we discuss how 24 to prove stability guarantees on the combination of a controller (that is unaware of deadline misses) 25 and its system-level implementation. We apply the proposed verification procedure to a synthetic 26 example and to an industrial case study. 27