Improved stability conditions for systems under aperiodic sampling: model- and data-based analysis

TL;DR

This paper refines stability analysis for systems under aperiodic sampling by precisely characterizing a delay operator, leading to less conservative conditions applicable with limited data or full models.

Contribution

It introduces an exact gain computation for the delay operator and improves stability conditions for data- and model-based analysis of aperiodic sampled systems.

Findings

Reduced conservativeness of stability conditions demonstrated in examples

Exact gain computation of the delay operator enhances analysis accuracy

Applicable to systems with limited noisy data or full model knowledge

Abstract

Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems were obtained by rewriting them as an interconnection of a linear time-invariant system and a delay operator, and subsequently, performing a robust stability analysis using a known bound on the gain of this operator. In this paper, we refine this approach: First, we show that the delay operator is input-feedforward passive and second, we compute its gain exactly. Based on these findings, we derive improved stability conditions both in case of full model knowledge and in case only data are available. In the latter, we require only a finite-length and potentially noisy state-input trajectory of the unknown system. In two examples, we illustrate the reduced conservativeness of the proposed stability conditions over existing ones.