Safety verification of real-time control systems with flexible timing

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This work analyzes control loops affected by input/output timing deviations, which can lead to increased control errors or instability. It presents methods for determining a safe tolerance band for these timing deviations, focusing on two approaches: stability analysis at design time and timing adaptation at run time. Both methods accommodate multiple inputs and outputs with individual timing uncertainties. For design-time analysis, the work offers techniques to assess stability and maximal control error for a specified input/output time window, utilizing linear impulsive systems for linear cases. Progress is made on nonlinear cases through reachability analysis of hybrid automata combined with the Continuization method. Additionally, a framework for flexible run-time adaptation is developed using convergence rate abstractions. This allows decisions on permissible input/output timing based on the current situation with minimal computational overhead. Consequently, larger temporal deviations can be tolerated temporarily, provided that long-term average timing remains adequate to ensure stability. The analysis thus addresses both theoretical and practical aspects of maintaining control system stability amidst timing uncertainties.