Delay-scheduled state-feedback design for time-delay systems with time-varying delays—A LPV approach

This paper is concerned with the synthesis of delay-scheduled state-feedback controllers which stabilize linear systems with time-varying delays. In this framework, it is assumed that the delay is approximately known in real-time and used in the controller in a scheduling fashion. First, a new model transformation turning a time-delay system into an uncertain LPV system is introduced. Using this transformation, a new delay-dependent stability test based on the so-called full block S -procedure is developed and from this result, a new delay-dependent stabilization result is derived. Since the resulting LMI conditions depend polynomially on the parameters, a relaxation result is then applied in order to obtain a tractable finite set of finite-dimensional LMIs. The interest of the approach resides in (1) the synthesis of a new type of controller scheduled by the delay value which has a lower memory consumption than controllers with memory (since it is not necessary to store past values of the state), and (2) an easy consideration of uncertainties on the delay knowledge.