Robust <I>H<sub>∞</sub> </I>Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators

Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust <I>H<sub>∞</sub></I> controller, which ensures robust asymptotic stability of the system as well as a desired <I>H<sub>∞</sub></I> performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the <I>H<sub>∞</sub></I> state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.