Analysis of Real-Time Control Systems using First-Order Continuization

Experience Report: Real-Time control systems can be difficult to analyze due to the mixture of discrete-time and continuous-time dynamics. This difficulty is particularly pronounced if the timing is non-periodic, e.g., due to network or execution effects. Still, most control loops behave similar to a purely continuous-time system disturbed by a small discretization error, which is exploited by Bak and Johnson (2015) in the method of Continuization. This paper uncovers limitations of that work and presents an extension, First-Order Continuization, based on a new formal framework that recovers previous results and eases future development.