Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays - A LPV Approach

Corentin Briat (1) , Jean-François Lafay (2) , Olivier Sename (1)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

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 interests of the approach resides in 1) the synthesis of a new type of controllers 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.

Domaines: Automatique / Robotique

Corentin Briat, Jean-François Lafay, Olivier Sename. Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays - A LPV Approach. Systems and Control Letters, 2009, 58, pp.664-671. ⟨10.1016/j.sysconle.2009.06.001⟩. ⟨hal-00402238⟩