Sampled-data control of linear parameter varying time-delay systems using state feedback

A sampled-data system includes the combination of continuous-time and discrete-time signals within the framework of hybrid dynamical systems. In this paper, we address the sampled-data control design problem for linear parameter varying (LPV) systems with state delay. The design objective is to find a discrete-time controller to ensure the closed-loop system stability and a prescribed level of performance, which in this study is defined to be the ℋ_∞ norm of the closed-loop system. Presence of the state delay in the system dynamics, as well as the hybrid structure of the closed-loop system due to the augmentation of the continuous-time plant and discrete-time controller calls for a new control strategy. To this aim, we utilize one of the most recently developed and less conservative approaches in designing a gain-scheduled controller for state-delay LPV systems to formulate the design problem in terms of a set of linear matrix inequality (LMI) conditions. To this end, we utilize the input delay approach to map the closed-loop hybrid system into a continuous-time one by introducing a new delay term in the original state delay plant. The effectiveness of the proposed method is examined through numerical simulation on a mechanical system.