Stabilization of linear systems with distributed infinite input delays: A low gain approach

Abstract

This paper investigates the stabilization problem of linear systems with distributed infinite input delays. By introducing a stability result on systems with infinite delays, it is shown that a stabilizable linear system with distributed infinite input delays can be globally asymptotically stabilized with low gain controllers as long as the open-loop system is not exponentially unstable. Our result includes constant delay and bounded distributed delay as its special cases. It should be noted that the stabilization problem of systems with distributed infinite input delays, to our best knowledge, has not been considered in existing literatures. Simulation examples are provided to illustrate the effectiveness of our theoretical results.