Delay-Independent L1 Controller for Linear Systems with Time-Varying Delay

It is a well-stablished theory that stability analysis and design of time-delay systems are not an easy task to deal with especially when the delay is time varying. In this article, a new delay-independent controller is introduced. The sub-optimal criterion proposed in this paper is independent of delay volume and its variation rate. The method proposed in this article takes advantage of L1 small gain theory and its applications to stabilize linear time-delay systems. In this document, the delay modeled as an uncertainty where its 1-norm is lower than one. Reducing the L1 norm of the closed loop system is transformed into a matrix inequality problem and the controller is evaluated using LMI method.