Efficient stability analysis approaches for nonlinear weakly-hard real-time control systems

This article considers the stability analysis of nonlinear control systems with failures in the feedback loop that satisfy weakly-hard real-time (WHRT) constraints. Such WHRT constraints are window-based guarantees like for example, that the feedback loop is at least closed for n times in each window of m sampling times. WHRT constraints can, e.g., describe the packet loss properties of a communication network. We consider two different actuation strategies to deal with failures in the feedback loop: holding the last received input or setting the input to zero if no new input arrives. We present stability analysis procedures for both strategies. The procedures are based on the emulation of a sampled-data controller from continuous-time feedback. For the hold strategy, we use a graph description for the WHRT constraints and a modified version of the Viterbi algorithm to bound a Lyapunov function candidate. For the zero strategy, we employ a bound on the evolution of the Lyapunov function candidate for zero input. For both strategies, efficient stability analysis procedures based on non monotonic Lyapunov functions are derived. In addition, we demonstrate how switched controllers, that switch depending on the past dropout sequence, can be used for the hold strategy. Such switched controllers can significantly increase the maximum allowable sampling period for the hold strategy. The proposed approaches are illustrated with a numerical example. (C) 2021 Elsevier Ltd. All rights reserved.