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

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 inputfeedforward 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.

Data-driven Control of Dynamic Event-triggered Systems with Delays

“…in [18], Lemma 1 enjoys reduced computational complexity and robustness against additive noise. Besides, thanks to its form of linear matrix inequalities, the databased representation (9) can be naturally married with modelbased sampled-data control methods, such as the discretetime approach, input-delay approach, input-output approach, and impulsive systems approach, to study data-driven control of sampled-data systems; see, e.g., [29], [27], [28]. Overall, the work of [29] put forward a unifying data-driven control framework for continuous-time sampled-data systems with time delays.…”

“…An extension studying data-driven system stabilization as well as robustness guarantees of systems with time-delays and measurement noise was recently investigated in [26]. Moreover, data-driven approaches for estimating the MSI and designing sampled-data controllers under aperiodic sampling were developed in [27] and [28]. Wedding the data-driven system representation in [21] with the time-delay approach, a data-based stability condition for continuous-time sampled-data control systems was derived in [29], along with a controller design proposal.…”