Reduction Model Approach for Linear Time-Varying Systems With Delays

Abstract

We study stabilization problems for time-varying linear systems with constant input delays. Our reduction method ensures input-to-state stability with respect to additive uncertainties, under arbitrarily long delays. It applies to rapidly time-varying systems, and gives a lower bound on the admissible rapidness parameters. We also cover slowly time-varying systems, including upper bounds on the allowable slowness parameters. We illustrate our work using a pendulum model.