Details and Proofs for: Stability Analysis of Multivariable Digital Control Systems with Uncertain Timing

Abstract: The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze stability under mostly-periodic timing with bounded uncertainty, a timing model typical for the implementation of controllers that were actually designed for strictly periodic execution. In contrast to existing work, we include the case of multiple sensors and actuators with individual timing uncertainty. Our approach is based on the discretization of a linear impulsive system. To avoid the curse of dimensionality, we apply a decomposition that breaks down the complex timing dependency into the effects of individual sensor-actuator pairs. Finally, we verify stability by norm bounding and a Common Quadratic Lyapunov Function. Experimental results substantiate the effectiveness of our approach for moderately complex systems.