Stability analysis and predictor feedback control for systems with unbounded delays

This paper proposes a novel general framework with new Lyapunov stability theorems for control problems of systems with unbounded delays. Under this framework, the delayed input can be captured in the stability estimate by augmenting it as a state with initial conditions. Then by applying the novel framework, we consider the stabilization problems of linear systems with distributed unbounded input delays via the so-called predictor feedback controllers. Both time-invariant and time-varying cases are considered. It is shown that under the new framework, the previous works on low-gain based truncated predictor feedback controllers can be improved by removing an implicit assumption on initial conditions. It is also shown that the predictor feedback controllers can exponentially stabilize both time-invariant and time-varying linear systems with distributed unbounded input delays. Several examples are provided to illustrate the effectiveness of the predictor feedback controllers.