Control-System Stability Under Consecutive Deadline Misses Constraints

Authors Martina Maggio , Arne Hamann, Eckart Mayer-John, Dirk Ziegenbein

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Author Details

Martina Maggio
  • Saarland University, Department of Computer Science, Saarbrücken, Germany
  • Lund University, Department of Automatic Control, Sweden
  • Robert Bosch GmbH, Renningen, Germany
Arne Hamann
  • Robert Bosch GmbH, Renningen, Germany
Eckart Mayer-John
  • Robert Bosch GmbH, Renningen, Germany
Dirk Ziegenbein
  • Robert Bosch GmbH, Renningen, Germany


This research was developed while Martina Maggio was on sabbatical at Robert Bosch GmbH.

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Martina Maggio, Arne Hamann, Eckart Mayer-John, and Dirk Ziegenbein. Control-System Stability Under Consecutive Deadline Misses Constraints. In 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 165, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Computer systems organization → Embedded and cyber-physical systems
  • Mathematics of computing → Mathematical analysis
  • Computer systems organization → Dependable and fault-tolerant systems and networks
  • Real-Time Control
  • Deadline Misses
  • Weakly Hard Models


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