Stochastic Aperiodic Control of Networked Systems with i.i.d. Time-Varying Communication Delays

TL;DR

This paper investigates the stochastic stabilization of networked control systems with i.i.d. time-varying delays, providing a necessary and sufficient condition for controller design that ensures stability despite unbounded delays.

Contribution

It introduces a novel stabilization criterion for NCS with unbounded, stochastic delays, extending control theory to more realistic network conditions.

Findings

Derived a necessary and sufficient inequality condition for stabilization.

Validated the theoretical results through numerical simulations.

Abstract

This paper studies stochastic aperiodic stabilization of a networked control system (NCS) consisting of a continuous-time plant and a discrete-time controller. The plant and the controller are assumed to be connected by communication channels with i.i.d. time-varying delays. The delays are theoretically not required to be bounded even when the plant is unstable in the deterministic sense. In our NCS, the sampling interval is supposed to be determined directly by such communication delays. A necessary and sufficient inequality condition is presented for designing a state-feedback controller stabilizing the NCS at sampling points in a stochastic sense. The results are also illustrated numerically.