Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective

In this paper we analyze a neuromorphic controller, inspired by the leaky integrate-and-fire neuronal model, in closed loop with a single-input single-output linear time-invariant system. The controller consists of two neuronal variables and generates a spiking control input. A spike is emitted by the controller whenever one of the neuronal states reaches a threshold. The control input is different from zero only at the spiking instants and, hence, between two spiking times the system evolves in open loop. Exploiting the hybrid nature of the integrate-and-fire neuronal dynamics, we present a hybrid modeling framework to design and analyze this new controller. In the particular case of single-state linear time-invariant plants, we prove a practical stability property for the closed-loop system, we ensure the existence of a strictly positive dwell-time between spikes, and we relate these properties to the parameters in the neurons. The results are illustrated in a numerical example.