On the stability of event-based control with neuronal dynamics

TL;DR

This paper analyzes the stability of event-based control systems with neuronal dynamics, establishing conditions for practical stability and linking them to analogue control stability properties.

Contribution

It demonstrates a fundamental connection between event-based impulsive control with neuronal units and traditional analogue control, providing stability guarantees.

Findings

Proves global practical stability for the event-based system.

Shows ISS-based stability guarantees in nonlinear cases.

Establishes practical exponential stability for linear systems.

Abstract

Event-based control, unlike analogue control, poses significant analytical challenges due to its hybrid dynamics. This work investigates the stability and inter-event time properties of a control-affine system under event-based impulsive control. The controller consists of multiple neuronal units with leaky integrate-and-fire dynamics acting on a time-invariant, multivariable plant in closed loop. Both the plant state and the neuronal units exhibit discontinuities that cancel if combined linearly, enabling a direct correspondence between the event-based impulsive controller and a corresponding analogue controller. Leveraging this observation, we prove global practical stability of the event-based impulsive control system. In the general nonlinear case, we show that the event-based impulsive controller ensures global practical asymptotic stability if the analogue system is input-to-state stable (ISS) with respect to specific disturbances. In the linear case, we further show global practical exponential stability if the analogue system is stable. We illustrate our results with numerical simulations. The findings reveal a fundamental link between analogue and event-based impulsive control, providing new insights for the design of neuromorphic controllers.