Using Delay for Control

Abstract

This article reviews two techniques that use delay for control: time-delay approaches to control problems (which initially may be free of delays) and the intentional insertion of delays into the feedback. We begin with a now widely used time-delay approach to sampled-data control. In networked control systems with communication constraints, this is the only method that accommodates transmission delays larger than the sampling intervals. We present a predictor-based design that enlarges the maximum allowable delay, which is important for practical implementations. We then discuss methods that use artificial delays via simple Lyapunov functionals that lead to feasible linear matrix inequalities for small delays and simple sampled-data implementations. Finally, we briefly present a new time-delay approach—this time to averaging. Unlike previous results, this approach provides the first quantitative bounds on the small parameter, making averaging-based control (including vibrational and extremum-seeking control) reliable.